The blasts come days after the government extended its control of the city with the implementation of a truce deal in Waer, the last insurgent-held area of Homs.
A vehicle bomb exploded close to a hospital in the mainly Alawite neighbourhood of al-Zahra in the east of the city, the Syrian Observatory for Human Rights monitoring group said.
The second large blast, originally suspected to have been a bomb, appeared to have come from an exploding gas canister and wounded people who had come to tend to victims of the first explosion in the densely-populated neighbourhood, state media said.
State television had earlier described the attack as "two large terrorist explosions". News agency SANA said the vehicle bomb had been packed with 150 kg of explosives.
Footage on state television showed a chaotic scene with black clouds of smoke rising above twisted metal debris. People stumbled over the rubble as they tried to ferry people away from the site.