Elon Musk is having himself quite a week -- he put 2 homes on the market, he's potentially shooting a movie in space with Tom Cruise, and oh yeah ... he had a baby with his girlfriend, Grimes.

The Tesla honcho revealed the news on Twitter Monday evening by first replying to a tweet by saying the birth was a few hours away, then following it up by tweeting ... "Mom & baby all good."

Soon after, he responded to a request for a baby pic with a shot of him holding his newborn son ... which he claims shall be named "X Æ A-12 Musk." He also posted one later of his kid with some "savage" face tattoos via social media filters.

The baby is the first for Grimes and the sixth for Musk. He has five sons -- a set of twins and a set of triplets -- from his previous marriage to author Justine Wilson.

As we've reported ... there hasn't been a dull moment with Elon the past week or so, especially on Twitter. He's been pushing to "free America now" amid the coronavirus pandemic, and has vowed to sell "almost all physical possessions" and not own a house.

He seems to be walking the walk too ... because he just put a pair of his Bel-Air mansions on the market this weekend.

As for that movie in space with Tom Cruise ... the actor and Musk's Space X are working with NASA on an action-adventure flick that would actually be shot in outer space, according to a Deadline report.

It's apparently in the early stages of development ... just like Musk's newborn son.

Like we said -- never a dull moment.