The bombing caused extensive damage to the hospital, about 50 km (30 miles) from the front line, the source said.
Two other attempted suicide bombings against forces positioned just outside the centre of Sirte did not cause casualties, he said.
Brigades aligned with Libya's UN-backed Government of National Accord (GNA) have made rapid advances over the past month. This week they entered Sirte, engaging Islamic State militants in street battles and targeting them with air strikes.
The brigades, made up mainly of fighters from the western city of Misrata, have faced suicide bombings, snipers and mines.
At least 120 brigade members have been killed and more than 500 wounded, security and hospital officials say.