Activists say about 35 pro-government fighters were killed and some medical staff taken hostage. More than 20 IS fighters were also reported killed.
The attack was centred on al-Assad hospital, to the west of the city.
Government forces retook the hospital after several hours, reports say, but the fate of the hostages is unclear.
BBC Arab Affairs Editor Sebastian Usher says the latest offensive shows that IS, despite recent setbacks, can still threaten significant government territory.
IS controls more than of half of Deir al-Zour and is seeking to capture the entire city.
The group has been besieging government-held areas there for two years, trapping about 200,000 civilians.
IS's Amaq news agency said its fighters had carried out a "major offensive" in Deir al-Zour early on Saturday, storming the hospital and cutting the route between a Syrian army base and the city's airport.
It said it had also taken over a fire station, university accommodation, grain silos and territory near the al-Tayyam oil fields.
A UK-based opposition news service, the Syrian Observatory for Human Rights, says government forces retook the hospital after several hours of fierce fighting.
Deir al-Zour is in an oil-rich area and on a vital supply route to the IS stronghold of Raqqa.
Militants from the Islamic State (IS) group have briefly overrun a hospital complex in the eastern Syrian city of Deir al-Zour, reports say.