Jade, who is married to fellow 'Bachelor' alum Tanner Tolbert, says she suddenly went into labor Monday night at her home ... but she couldn't make it out of the house, let alone to a hospital, so she gave birth in the closet in her master bedroom!!!

As you can see ... Jade is surrounded by medics and firefighters, holding her newborn son as she sits in her closet, surrounded by shoes, clothes and drawers. A wild scene, for sure.

Jade says it was one of the scariest moments of her life ... and she's still trying to process what the hell happened.

The good news ... Jade and Tanner's baby boy is healthy ... and he was 7 lbs., 9 oz and 20 inches long at birth.

Jade and Tanner met on the second season of "Bachelor in Paradise" ... and they have another child together, one-year-old Emmy. But, she was NOT born in a closet.