"Both mother and daughter are doing well," Robinson said in a prepared statement.
The name Suri has its origins in Hebrew, meaning "princess," or in Persian, meaning "red rose," the statement said.
The baby was born in Los Angeles but the exact location was not disclosed.
It's the first child for Holmes, 27. Cruise, 43, has an adopted daughter and son from his marriage to Nicole Kidman
Details surrounding the birth, which was planned under the tenets of the Church of Scientology as a silent procedure, weren't disclosed.
Outside the Beverly Hills home where Cruise and Holmes live, about a dozen reporters and photographers stood by. Security officers inside the compound videotaped the journalists.
A security guard at the gate refused to release any information. A few cars did arrive and were allowed into the estate. A police motorcycle officer stopped by around 4 p.m. and sat watching the goings-on.
The patrolman, who identified himself as Officer Chase, said he was just making a routine check, since activity around the area had been heightened for some time. He asked if the baby had been born, was told yes, and drove off.