Kabul police spokesman Basir Mujahid said hundreds of people were inside watching a match when the bomber struck outside the gates where security guards were searching people.
Health Ministry official Mohammad Salim Rasouli confirmed the death toll, saying at least seven other people were wounded.
No one claimed responsibility for the attack.
The stadium was packed with people watching the Shpageeza Cricket League 2017, Afghanistan's annual domestic T20 Tournament.
The Tournament, which features six teams, started on Sep. 11 and runs through Sept. 22. All the teams have foreign players, mainly from Sri Lanka, Zimbabwe and South Africa.
The match was on a break while the attack happened, but resumed without delay.
On Aug. 29, a suicide bombing in a busy commercial area in Kabul near a string of banks and not far from the US Embassy killed at least five people. The Taliban claimed responsibility for that attack.
Both the Taliban and an Islamic State affiliate have carried out previous attacks in Kabul.