Meta's Muse AI personal agent tool has only been out for nearly two weeks, and it's topping the app store charts.

The social media giant's Muse app is currently ahead of popular services like OpenAI's ChatGPT, Polymarket and Kashi on Apple's iOS app store for the category of free smartphone programs in the U.S. as of Monday. It's also ahead of rival AI apps like Anthropic's Claude and SpaceXAI's Grok AI, in addition to the Facebook-parent's own Meta AI app.

The Muse app overtook ChatGPT as the leading iOS free app in the U.S. on Friday, and racked up 730,000 downloads over about five days after it launched on Sep. 8, according to the analytics firm Sensor Tower. As of Monday, Muse has logged over 2.5 million downloads since its debut, the market intelligence company said.

Muse's cumulative downloads topped Claude and Grok during the same 13-day post-launch window, with those apps recording 400,000 and 200,000 downloads, respectively. ChatGPT obtained 3.1 million downloads during that time frame, Sensor Tower said.

The firm noted that the apps had staggered platform releases split between Apple and Google Play, which would impact their totals. Sensor Tower said that as of Monday, Muse has garnered around 1.5 million and 1.1 million downloads on the iOS and Android app stores.

Meta pitched the app as a way for consumers to manage and direct supercharged digital assistants that can perform a number of tasks across the web, like filling out electronic forms and organizing email inboxes. The app, which is powered by Meta's Muse Spark family of AI models, represents a major push by CEO Mark Zuckerberg into the AI agent market, which the freely available OpenClaw tool helped popularize earlier this year among developers and technology enthusiasts.

"I think up to this point most of the agentic use cases have not really been for normal people," Bernstein analyst Stacy Rasgon told CNBC in a "Squawk on the Street" interview on Monday. "Now you've got Meta's Muse and other agents out there that are starting to maybe get more potential for more broad-based adoption."

The buzz around Meta was also reflected in the stock, which surged more than 11% on Monday. Wells Fargo lifted its price target on the company's stock to $796, according to multiple reports.

Although people can use the Muse app for free, Meta is also offering monthly subscriptions that will cost $20 or $100, depending on usage. It's a way for Meta to potentially make money off AI agents that isn't centered on the company's core online advertising business.

But Meta's debut of Muse comes amid broader societal concerns around AI's safety and cybersecurity risks that have rocked the tech industry over the past few weeks. Meta also recently agreed to pay roughly $17 billion to settle with a coalition of state attorneys general that had sued the company for misrepresenting alleged harms to children and teenagers caused by apps like Facebook and Instagram.

It's unclear how long the Muse app will remain a hit, considering that other AI services have experienced similar boom times upon their release but failed to remain blockbusters, such as OpenAI's Sora and Meta's Vibes AI video tool, which helped bolster downloads of the Meta AI app when it was first released last September.

"They care about security, I don't know how much they care about privacy," Rasgon said, referring to whether the personal data-hungry Muse app will sting Meta in the long run.

The growing popularity of these agents is having ripple effects on the places they visit online, and e-commerce giant Amazon has blocked Muse from accessing its shopping site, citing privacy and security risks.

Amazon said it was not given advanced notice that Muse would access its store and outlined several other concerns. The company said the agent bypasses the personalization and other features built into the shopping experience and said Muse appears to capture and store customer credentials and scrape account data.

"We think it's fairly straightforward that third-party applications that offer to make purchases on behalf of customers from other businesses should operate openly and respect service provider decisions about whether or not to participate," an Amazon spokesperson said in a statement.

GeekWire was first to report on the move by Amazon.

Shopify, however, is working with Meta on Muse access. Shopify CEO Tobias Lütke announced Monday that the e-commerce site was partnering with Muse to allow agentic checkout in its online stores.

WATCH: What Meta's Muse means for AI.