The blaze started at the ICL UK Boulby mine at 00:30 BST on 13 April, 1,100m (3,600 ft) under the sea bed and five miles (8km) from land.
Seven workers were taken to hospital and treated for smoke inhalation.
The Health and Safety Executive (HSE) said a notice had been served in relation to the underground fire.
More than 100 staff were underground at the time, 11 of whom were temporarily unaccounted for.
Polystyrene blocks are believed to have caught fire in the mine.
A spokesman for ICL UK, said: "We have been working closely with HM Mines Inspectorate in the investigation into the recent incident.
"Safety is always our first priority and we are fully committed to working with the inspectorate in order to identify ways in which procedures can be improved.
"We will, of course comply with all the measures set out in the improvement notice."
The company has until 27 June to comply with the notice.
The HSE said the investigation was ongoing.
One of Europe's deepest mines, the site employs about 1,100 people.
Last year, the company announced it was shedding hundreds of jobs as part of a "new business strategy" to produce fertiliser polysulphate.

A lawyer for the former Cleveland Browns quarterback told the Associated Press news agency that prosecutors had told him a charge was coming.
A Texas grand jury has agreed a misdemeanour assault charge for family violence, the lawyer said.
Colleen Crowley says he confronted her at a Dallas hotel and hit her as they drove back to Fort Worth.
The Class A misdemeanour carries up to one year in jail and a $4,000 fine.
Lawyer Robert Hinton told AP the charge was expected on Tuesday and he expected a judge to set bail.
Despite success playing football as a university student, Manziel - nicknamed "Johnny Football" - has struggled with substance abuse and personal issues in the professional league.
Manziel was released from Cleveland Browns in March.

Bianca Nikol Roberson, a recent school graduate, was driving near West Goshen when her car veered off the road.
Police responded to what they initially thought was a fatal collision, but then discovered that Ms Roberson had been shot in the head.
Investigators believe another driver shot her as she attempted to merge into the same lane as a red pickup truck.
The road on which Ms Roberson was driving narrows to a single lane where it joins another main route.
"Her car started jostling with a red pickup truck - not actually hitting - but both of them trying to merge together," prosecutor Tom Hogan told reporters.
"And then she was shot. The man in the red pickup truck shot her directly in the head."
"This was a senseless and brutal act of violence," he added.
Ms Roberson was pronounced dead at the scene. The case is now being treated as a homicide.
Police have issued a call for help in tracing the pickup truck and the suspect, who is described as a white male aged between 30 and 40 with blonde hair and a medium build.
Mr Hogan said "every cop in three states" is looking for the vehicle.
Ms Roberson's father, Rodney, spoke to NBC News about his daughter, telling them she was preparing to attend university.
"We were all excited for her," he told the station. "She was excited. We were just happy for her."
Her brother, Dontae Arburg, said she was "very loved."
"She always smiled. Always wanted to entertain and make you smile," he said.
A potash mine in East Cleveland has been issued with an improvement notice after a fire broke out hundreds of metres below the sea bed.
[NEXT_CONCEPT]
Troubled NFL quarterback Johnny Manziel is expected to be charged over an alleged assault on his ex-girlfriend.
[NEXT_CONCEPT]
Pennsylvania police are hunting a man who shot and killed an 18-year-old girl in a "road rage incident".