Some users reported seeing a message that they were locked out but were still able to scroll through their feeds.
Others posting on Twitter said they were completely shut out.
Some reported that their number of followers dropped, presumably because those accounts were locked.
The number of people complaining of being locked out of their accounts began to spike about 11.30pm on Monday AEDT.
It was unclear whether the problem was an internal issue or whether the social media site had been hacked.
“We are aware that some Instagram users in different parts of the world are having issues accessing their Instagram accounts,” a spokesperson for Meta said.
“We’re working to resolve the issue as quickly as possible and apologise for the inconvenience.”
Users flooded social media platforms about the issue and Instagram acknowledged the problem on Twitter at 1.14am AEDT.
In a couple of hours, the tweet had received more than 14,000 comments and was retweeted more than 40,000 times.