West Yorkshire Police have put on extra patrols in the Hanover Square area of the city after anonymous and offensive letters - titled "Kill Scum Muslims" - were posted through doors.
There are concerns that the letter will raise tensions as the English Defence League (EDL) prepares for a demonstration in nearby Keighley on Saturday.
The leaflets said women wear burkas because they are ugly and claimed men are grooming white girls in the area.
The letter said: "We are now going to do acid attacks on anyone who wears the funny black masks around your square and Bradford and other places."
Campaign group Just Yorkshire condemned the letters and it was concerned for local people, "particularly those who are visibly Muslim".
Chairman Nadeem Murtuja said: "I am extremely concerned that there are now Muslims in this country that are having to shave their beards and remove their hijabs - taking away the very freedoms that form the cornerstone of British values and the right for people to practise their faith freely, evidenced by the fact that Islamophobic and racist-driven hate has increased five-fold in the last five years.
"This is a time for calm heads, and people in positions of power, locally and nationally, need to become more visible in their stance towards protecting the human rights of all communities, including the Muslim community."
A police spokesman said: "West Yorkshire Police have commenced an investigation following reports of offensive literature being circulated in the Hanover Square area.
"The incident is being treated as a hate crime and being taken extremely seriously.
"A thorough investigation has been launched and officers are working with the local community and partners to identify and prosecute those responsible for this despicable crime.
"We understand the impact hate crime and hate incidents can have on our communities and on individuals, and crimes of this nature will not be tolerated.
"Additional patrols have been deployed to the area following this report and police are working with local leaders to reassure residents, and to trace those responsible."