Homeowners hit by the flooding in December can apply for up to Â£5,000 from the government's Future Flood Prevention Funding scheme.
Figures seen by the BBC show that only 13 people have applied for the money.
Rachael Maskell, Labour MP for York Central, said she had received complaints about accessing the fund.
"The form filling is incredibly complicated and that's where people have been struggling," she said.
"It's putting off a lot on people."
Hundreds of homes and businesses were flooded in the city after the Rivers Foss and Ouse burst their banks.
The scheme is administered by City of York Council and requires a survey to be carried out on the flooded property before funding can be applied for.
The council said that 360 private homes were eligible for the grant.
The authority added: "We very much welcome grant applications but know that this can take time while people wait for quotes and loss adjustor reports.
"We're appointing a case worker to help residents and businesses through the application process."

Prince Charles did not mention the Islamic State group but his comments at Sandhurst are being interpreted as a reference to the organisation.
He told the cadets the international order was "under challenge as never before in my lifetime".
It was the first passing out involving mixed platoons of men and women.
The Sovereign's Parade at the military academy in Surrey formally marks the senior cadets' completion of their commissioning course, and the Prince of Wales was representing the Queen at the event for a fourth time.
He told the officer cadets they would face trials "as great as any faced by our forebears", but said he was confident they would rise to the challenge.
"You are receiving your commissions as officers at a moment when the profession of arms is moving into uncharted waters," he said.
"In the face of such challenges, Britain's traditional qualities - fair play, civility, a sense of humour in adversity - remains as precious as they've always been.
"The harder it becomes to stop people determined to maim and kill, the more urgent becomes our need to understand and defuse their perverse determination."
Among those watching the parade was tennis player Andy Murray's wife Kim, whose brother Scott Sears was passing out.
Prince Charles is colonel in chief of the Royal Gurkha Rifles and wore his Army field marshal uniform at the parade.
His speech came as the Ministry of Defence issued an update on RAF operations against IS targets in Iraq and Syria.
Officials said that on Thursday two Typhoon FGR4s struck an IS-held building and a bunker in northern Iraq with a Paveway IV guided bomb; a Tornado patrol destroyed a building and a mortar position with Paveways, and a Reaper drone struck a vehicle and supported Kurdish forces when they came under fire from a sniper.
On Wednesday, two Tornado GR4s provided air support to Kurdish soldiers fighting IS in northern Iraq, and used a Paveway IV guided bomb to destroy a position.

27 January 2015 Last updated at 14:30 GMT
They show that the asteroid has its own small moon orbiting it.
The asteroid passed by the Earth at a safe distance of 1.2 million km, giving scientists a rare chance to study it 'up close'.
The new data shows that asteroid 2004 BL86 is about 325m across, and its moon is around 70m wide.
Now that it has passed Earth the asteroid will continue on its orbit around the Sun, and it won't come this close again for another 200 years!
The next 'close shave' of a large asteroid is due in 2027: that object is called 1999 AN10 and is just over 1km wide.
York residents are being put off applying for flood protection grants as the process is "incredibly complicated", a local MP has claimed.
[NEXT_CONCEPT]
A "cult of death and destruction" is seducing "lost young people", the Prince of Wales has told Army officer cadets at a passing-out parade.
[NEXT_CONCEPT]
New pictures of asteroid 2004 BL86, which passed close by Earth yesterday, have been released by US space agency Nasa.