The tech company is recommending security updates that customers should apply immediately.
The FBI said it is aware of the attacks and is working closely with its federal and private-sector partners, but offered no other details.
In an alert issued on Saturday, US time, Microsoft said the vulnerabilities apply only to SharePoint servers used within organisations.
It said that SharePoint Online in Microsoft 365, which is in the cloud, was not hit by the attacks.
The Washington Post, which first reported the hacks, said unidentified actors in the past few days had exploited a flaw to launch an attack that targeted US and international agencies and businesses.
The hack is known as a "zero day" attack because it targeted a previously unknown vulnerability, the newspaper said, quoting experts. Tens of thousands of servers were at risk.
Microsoft did not immediately respond to a request for comment.
In the alert, Microsoft said a vulnerability "allows an authorised attacker to perform spoofing over a network". It issued recommendations to stop the attackers from exploiting it.
In a spoofing attack, an actor can manipulate financial markets or agencies by hiding the actor's identity and appearing to be a trusted person, organisation or website.
Microsoft said it issued a security update for SharePoint Subscription Edition, which it said customers should apply immediately.
It said it is working on updates to 2016 and 2019 versions of SharePoint. If customers cannot enable recommended malware protection, they should disconnect their servers from the internet until a security update is available, it said.
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