Elon Musk reportedly had twins on the low last year with a woman who is running one of his companies ... making him a father to at least 9 kids.

Elon had twins with Shivon Zilis -- a top executive at Neuralink, the brain chip company Musk co-founded and chairs -- according to an Insider report, and court docs filed in Texas.

The twins were born in November, and the timing is interesting ... because only a few weeks later in December, Elon and Grimes welcomed their second baby via surrogate.

No word on the twins' first names, but court docs were reportedly filed earlier this year by Elon and Shivon requesting the children's names be changed to include Zilis as a middle name, and Musk as the last. A judge already approved the request.

Elon and Shivon met back in 2015, and she's been rising through the ranks at his companies ... including a stop at Tesla before Neuralink. There's speculation Elon might pick her to run Twitter if his deal to buy the social media giant eventually goes through.

Elon's made a big fuss over the years about declining birth rates, and now he has 9 kids we know about ... including 5 with ex-wife Justine Wilson, 2 with Grimes and now 2 with Shivon.

As we reported, Elon and 4 of his kids recently met Pope Francis at the Vatican.

We reached out to Elon's camp about the twins ... so far no word back.