Mr Musk was responding to Microsoft’s plan to remove Twitter from its corporate advertising platform.
He did not provide further details or evidence to support the claim.
Microsoft declined to comment when approached by the BBC on Thursday.
Earlier, the company said in a notice that its advertising platform would “no longer support Twitter” from Tuesday 25 April.
As a result, ad buyers would not be able to access their Twitter accounts through Microsoft’s social management tool.
“Other social media channels such as Facebook, Instagram, and LinkedIn will continue to be available,” Microsoft said.
Twitter’s press email responded to a query with a customary poo emoji.
In a separate tweet, in the discussion about the social media platform’s data, Mr Musk said he was “open to ideas”.
“But ripping off the Twitter database, demonetizing it (removing ads) and then selling our data to others isn’t a winning solution,” he added.
In February, Twitter started charging for the data it collects from “hundreds of millions” of users, with a basic plan starting at $100 a month.
The data allows users to “manage and track every aspect of your social media presence”, according to the platform.
Since buying Twitter for $44bn (£35.4bn) in October, Mr Musk has cut its workforce by around 80% and moved to boost the company’s finances through measures including charging users for “blue tick” verification.
In recent months, major companies including iPhone maker Apple reportedly halted advertising on the platform over concerns about how content was moderated on the site.
In November, Mr Musk said Twitter had seen a “massive” drop in revenue and blamed activists for pressuring advertisers.
Speaking to last week, he said Twitter had just months left to live when he took over. He also said “almost all advertisers have come back or said they are going to come back” to Twitter.
Mr Musk added that Twitter could be profitable by the second quarter of 2023, and he would be willing to sell the company if the right person came along.