"According to preliminary investigations, the explosions were cases of man-made, deliberate sabotage," an unnamed spokesman from the city's police department, told AFP on Monday.
No further details were given.
Following the blasts, police cordoned off some streets in the area and conducted identity checks in a search for any "suspicious" persons, public security officials said in a statement.
The blasts come as China ramps up security ahead of next month's showcase Olympic games.
Chinese authorities have warned that the games could be the target of terrorist attacks and have pledged an unprecedented security effort.
Among measures announced are the deployment of a 100,000-member anti-terrorist force, along with anti-aircraft missile batteries near to key locations.
The Kunming explosions come two days after police in the same province, Yunan, opened fire and killed two rubber farmers in a clash that also saw 41 police officers injured.
The clash was sparked when police tried to arrest five people for allegedly attacking a local rubber company in a long-running dispute between farmers and the firm, state media said.
Chinese authorities have ordered local officials to keep a lid on grievances and try to resolve disputes to ensure a "harmonious social atmosphere" in the Olympics period.