First he criticised Twitter, and later said that Facebook is something he has not heard about in years.
"Twitter sucks," he tweeted.
When a user replied ‘much better than Facebook though', Musk replied: "[Slow drag on cigarette) Facebook? Haven't heard that name in years".
Musk's Twitter account was compromised by hackers who ran a Bitcoin scam on the platform, posting tweets that promoted the scam almost as fast as they were deleted.
Musk was the first hacking victim when a tweet was posted on the Tesla CEO's account, promising to double any payments sent to a Bitcoin address.
The Tesla CEO has faced similar Bitcoin scams under fake profiles on Twitter in the past.
In February, he slammed Twitter for the rise in trolling networks and scams via fake bots.
"The crypto scam level on Twitter is reaching new levels. This is not cool," Musk said.
"Report as soon as you see it. Troll/bot networks on Twitter are a *dire* problem for adversely affecting public discourse and ripping people off," he added.
Musk and Facebook CEO Zuckerberg have also been involved in public spat, especially over Artificial Intelligence (AI), in the past.
"I've talked to Mark about this (AI). His understanding of the subject is limited," Musk tweeted.
The tweet came after Zuckerberg castigated Tesla founder Musk for arguing that care and regulation was needed to safeguard the future if AI becomes mainstream.
In February this year, Musk said: "DeleteFacebook It's lame".