Investigators said the incident bore the hallmarks of an al Qaeda operation.
Policeman Fadel Ali said police cadets were leaving the college when the bomber attacked, saying: "We ran to the place and found dozens of cadets covered in blood. The scene was horrific."
Another witness said he saw a man in his 20s enter the crowd as cadets gathered near the academy. He said: "A loud explosion shook the area and I saw cadets on the ground."
The bombing in Sanaa followed a similar attack in the capital in May, when a suicide bomber in army uniform killed more than 90 people during a rehearsal for a military parade.
Theodore Karasik, director of research and development at the Institute for Near East and Gulf Military Analysis, said al Qaeda appeared to be adopting methods used in Iraq.