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."
York residents are being put off applying for flood protection grants as the process is "incredibly complicated", a local MP has claimed.