Skai Jackson announced she gave birth to her first child over the weekend -- but the father was MIA ... and for good reason -- he was locked up!

According to legal docs, Deondre Burgin has been cooling his heels behind bars at the Hamilton County Jail in Ohio since November and, as a result, Burgin was a no-show for the birth of his kid with Skai -- famous for her roles on Disney Channel sitcoms like "Jessie" and "Bunk'd."

Back in November, Burgin was given a 90-day sentence after he violated his parole from an earlier theft and weapon possession case as a juvenile, according to Hamilton County court records.

If all goes well, he should be out in February, so the happy dad would then presumably get to see his little one -- assuming things are still amicable with Skai.

As for Skai ... a family source tells TMZ she is "happy" about becoming a mother and that her baby boy Kasai is healthy. Our insider adds she's ready to be a working mom and is "determined to be the best mother and role model."

You may recall last August ... Skai was arrested for domestic battery after she allegedly pushed Deondre in Los Angeles. The L.A. County District Attorney later dropped the case because Deondre had no visible injuries and refused to cooperate.