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.

Barry Joy, 56 and Daniel Timbers, 28, died in a "fierce fire" following an explosion at digger bucket maker Harford Attachments in Norwich in 2015.
The coroner said Mr Timbers had been standing in for his father who was ill.
Post-mortem examinations said the men died as a result of the effects of fire and inhalation of fumes of combustion.
The inquest was told staff heard a "loud noise" at about 09:00 BST on 13 July 2015.
"Staff evacuated the premises, with some of them bravely trying to rescue Mr Timbers and Mr Joy," coroner Yvonne Blake told the Norwich inquest.
She added, "Their bodies were recovered from the booth afterwards."
Paint sprayer Mr Joy, of Spencer Street, Norwich and production operative Daniel Timbers, of Dereham Road, Norwich, were working in one of two booths bought from RAF Lyneham in Wiltshire when the base was closed down.
Kenneth Stedman, managing director of Ipswich-based Industrial Powder and Paint Services, advised Harford Attachments on the transaction.
The inquest heard the two units were "well kept for their age" and he advised the company that they would be suitable to be set up as they were on the airbase.
The coroner said the jury inquest, which is continuing, would hear evidence about training of staff, policies on site and extraction equipment on the paint-spraying booths.

They started arriving at Poldhu Cove on the Lizard on Sunday, and National Trust volunteers have been clearing them away as they are said to pose a risk to wildlife.
The bottles are sealed, but witnesses say some have leaked.
The National Trust said it believed a container had gone overboard from a ship, during the stormy weather.
The Maritime and Coastguard Agency said: "While it is fact that the MV Blue Ocean lost a container containing bottles of 'Vanish', there is no currently available evidence that the bottles washed up on the Cornish coast are from this container; all evidence is currently circumstantial."
It is thought the vessel lost the container near Land's End in May.
The BBC has contacted Vanish, but the company is yet to comment.
Other nearby coves including Gunwalloe, Polurrian, Church Cove and Marazion have also been affected, conservationists said.
Cornwall Wildlife Trust said it was "highly concerned" about the impact on "sensitive marine life".
Justin Whitehouse, from the National Trust, said: "The main worry is all that detergent going into our beautiful marine environment, but thankfully most are full.
"We think it's a container that has gone overboard from a container ship, during stormy seas."
Cornwall Council said the authority and partners, including the Maritime and Coastguard Agency and Natural England, would be monitoring beaches in the area.
It said: "The National Trust who own the beach at Poldhu have arranged for the bottles to be cleared away.
"In the meantime the public are advised to keep children and dogs at a safe distance from the bottles should any more be washed up.
"No attempt should be made to recover the bottles."
Militants from the Islamic State (IS) group have briefly overrun a hospital complex in the eastern Syrian city of Deir al-Zour, reports say.
[NEXT_CONCEPT]
Two men who died in a paint-spraying booth were so badly burned they could only be identified using their dental records, an inquest has heard.
[NEXT_CONCEPT]
Thousands of bright pink plastic detergent bottles have washed up on beaches in Cornwall.