The State Department said they are aware of five Americans who were injured in the.
One of them was 26-year-old Elaine Dang of Del Mar, Calif.
In a conversation with San Diego affiliate KFMB just after she got out of surgery, Dang said she was doing okay.
"I'm very grateful to be alive," Dang said. "I'm very greatful to the Kenyan people. They have been so helpful and supportive."
Dang said two of her friends were killed in the attack by the Somalia-based al-Qaeda-linked al-Shabab terrorist group.
The general manager for an online restaurant guide said she has had operations on her chest, arms and legs.