Paltrow's publicist confirmed the baby was born in New York during the weekend, but offered no further details, People magazine reported Monday.
The 33-year Oscar-winner and her Grammy-winning husband, 29, have a daughter, Apple, who turns 2 on May 14.
Martin is the frontman of Britain's Coldplay. "Moses" was the name of a song he wrote for Paltrow in 2003, People noted.
Celebrity Families of 2014 [PHOTOS]