ARK runs five exchange-traded funds that actively invest in companies Ms. Wood and her team of portfolio managers believe will change the world through what they call “disruptive innovation.” Among the ETFs’ biggest holdings are electric car maker

Tesla Inc.,

payments company

Square Inc.

and streaming media firm

Roku Inc.

The stock prices of those three companies have surged at least 195% in the year since the Covid-19 pandemic upended the investing landscape—helping ARK’s funds more than double over the same period. But the stocks dropped more than 12% last week amid a broader selloff in fast-growing tech stocks, a slump many attribute to a sharp rise in government bond yields.

They have badly underperformed the tech-heavy Nasdaq Composite Index, which dropped 4.9% last week.

Worries about a rising interest-rate environment have posed a test for ARK, exposing the vulnerabilities of its investment approach. Higher yields generally make growth stocks, including shares of big tech companies, less attractive. Plus, some of ARK’s positions are in small, illiquid stocks that have the potential to swing dramatically.

The ETFs suffered double-digit percentage decreases last week, their biggest routs since the stock market’s plunge last March, according to FactSet. Further declines among growth stocks on Tuesday and Wednesday drove even deeper drops among ARK’s funds, bringing the declines for its flagship ARK Innovation ETF to 14% over the past month.

The cascade of red has proved hard for many investors to stomach. ARK’s funds collectively lost more than $1.8 billion between Feb. 24 and Monday, their biggest stretch of outflows ever, according to FactSet. Together, they managed roughly $51 billion at the end of February, making ARK the ninth-largest ETF operator. That’s after attracting $36.5 billion in assets over the past year, more than

Invesco Ltd.

,

Charles Schwab Corp.

and First Trust—the fourth, fifth and sixth biggest ETF issuers in the U.S., according to Morningstar Direct.

But the recent outflows triggered sales across ARK’s funds to meet redemptions, while the firm also opted to dump shares of its easier-to-trade holdings, including

Apple Inc.

and

Snap Inc.,

to load up on favorites like Tesla.

With tech stocks continuing to fall, ETF analysts and traders worry that a combination of broad market declines and additional outflows could create a snowball effect across ARK’s portfolio. That could potentially cause some of its more illiquid, small-cap holdings to trade sharply lower.

Tom Staudt, ARK’s chief operating officer, dismissed concerns of any liquidity problems and said ARK’s ETFs have continued to perform as any other ETF would during the tumult.

Still, it has been a rough patch for ARK and its star stock picker, Ms. Wood.

“What a crazy week or two we’ve had here,” Ms. Wood said in a YouTube video posted Friday that was viewed by nearly 600,000 people.

Ms. Wood founded ARK in 2014 and now serves as its chief executive and chief investment officer following a 12-year stint at AllianceBernstein. Her funds’ eye-catching performance, coupled with her willingness to engage investors through social media, podcasts and videos, has earned her a variety of endearing monikers from individual investors and Reddit’s day traders, including “Mamma Cathie,” “Aunt Cathie” and, in South Korea, “Money Tree.”

“ARK’s funds fit 2020’s narrative of secular growth, but we’re now seeing a shift in that,” said Steven DeSanctis, an equities analyst at Jefferies. “It probably won’t be the last time in the near term she sees outflows,” Mr. DeSanctis added, referring to Ms. Wood.

Outside of last week’s pullback, ARK’s returns have been the envy of the asset-management industry, reviving some investors’ belief in stock pickers after more than a decade of dominance by index-tracking funds. The ARK Innovation ETF has logged an average annual return of 36% since it started trading in 2014. That compares with the S&P 500’s average return of 11% over the past 10 years.

“There’s been lots of calls with clients over the last six months as the funds gained assets, and the primary conversation has been about what happens when the funds are no longer a hot topic,” said William Kartholl, director and head of ETF trading at Cowen.

Mr. Staudt said ARK has a soft limit of about 10% on any one stock within its funds. Tesla’s stock sits at that level in ARK’s innovation and autonomous funds, as does Square in ARK’s fintech innovation pool. As for ARK’s exposure to smaller stocks, Mr. Staudt said those worries are overblown and pointed to the fact that about 15% of ARK’s innovation fund is invested in stocks with market caps below $5 billion.

If anything, the volatility has created “attractive buying opportunities” for ARK, Mr. Staudt added.

ARK loaded up on more shares of Tesla,

Teladoc Health Inc.

and Square during last week’s selloff, according to ARK’s daily trading logs. It also added more shares of

Zoom Video Communications Inc.

to one of its funds earlier this week.

Amid the redemptions across ARK’s funds, the firm also sold shares in some of its more widely traded liquid stocks. The firm cut its positions in Apple and Snap last week and sold all its remaining shares in

Salesforce.com Inc.,

he added. ARK also sold shares of

Facebook Inc.,

Bristol-Myers Squibb Co. and

Roche Holding AG

this week.

“It’s almost like having dry powder in the portfolio,” said Mr. Staudt, referring to how the funds basically build up a cash-like reserve to buy other stocks.

Not all investors are fazed by ARK’s bigfooted approach to investing. Flows into ARK’s innovation fund turned positive Tuesday, pulling in $464.3 million, according to FactSet.

But ARK’s most recent stumble continued to shake out others.

Paolo Campisi, a 31-year-old entrepreneur in Toronto, bought shares of ARK’s innovation fund in early February but sold his stake last week after shares dropped more than 10%. He decided to take a riskier bet on an eventual rebound by buying out-of-the money call options that expire at the end of the month. But he sold those options as well Wednesday when ARK’s flagship fund fell an additional 6.3%.

“I think everyone’s going to be challenged moving forward,” Mr. Campisi said, adding that he is unsure at what level he’d consider buying back into the fund again. “And the level of scrutiny on someone like Cathie [Wood] is going to be high.”

Write to Michael Wursthorn at Michael.Wursthorn@wsj.com