It is unclear what the problem is, though people took to social media in their droves to complain about the outage.
Microsoft said in a brief statement: "We are aware of reports that some users are having difficulty signing in to some services.
"We are investigating this issue."
A spokeswoman was unable to provide any further details when asked about the scale of the outage or how long it might take to fix.
Hotmail, which has been rebranded under Microsoft's Outlook banner, is believed to have crashed before midday GMT.
The company responded to one user in Ireland (Other OTC: IRLD - news) : "Sorry for the inconvenience. We know about the issue and are currently working on the resolution. Request you try and log in again after a few hours."
Another user wrote on a Microsoft community site: "I've had repeated issues in the last 15 mins logging into Hotmail -first it said my account doesn't exist and then it says that my account can't be located, and then finally it asks for my password but the page doesn't look legit."
Some people who were experiencing problems were later able to log in again.
One user complaining on Twitter received a reply from Outlook saying it "should be up and running by now".
It comes months after Microsoft disclosed details of cyber attacks by a hacking group that exploited a security flaw in its Windows operating system.
The disclosure in November revealed that a group previously linked to the Russian government and US political hacks was behind the attacks.
It said at the time that it was issuing a new "patch" to protect Windows against the newly discovered threat.
Microsoft has not said what might be behind the latest problems.