"The first went into a container at the first checkpoint into the property where they check IDs. There he blew himself up.
"The other two then ran on into the main area which went on to the second checkpoint which enters the main house and office of the governor. There they started firing and there was a second explosion.
"It's believed the second suicide bomber blew himself up. We don't know the whereabouts of the third."
An interior ministry spokesman said: "Three heroic policemen have been martyred and three others injured."
Kandahar, the birthplace of the Taliban movement in the 1990s, is in a part of Afghanistan that has seen escalating attacks by the group, which was toppled from power by US-led forces in 2001.
Tooryalai Wesa, Kandahar's governor and the target of Saturday's attack, is an Afghan-Canadian academic. He has held the post for less than a year.