Sir Peter Fahy is concerned the force "will not be able to deploy enough officers and PCSOs into the local community to gather intelligence".
GMP has lost 1,100 officers since 2010, leaving about 6,800.
Policing Minister Mike Penning said there was "no question" police would have enough resources to do their work.
In 2010, GMP said 3,100 jobs - 1,500 officers and 1,600 civilian workers - had to go over a four-year period to meet the government's 25% spending cuts.
Sir Peter said: "It's really pretty stark now.
"I can't reduce much further the number of officers for instance investigating rapes and domestic violence.
"We then have to look at day-to-day neighbourhood policing and that is the risk - we end up being a reactive police force.
"We need to be in communities, preventing things before they happen."
Tony Lloyd, Greater Manchester's Police and Crime Commissioner, said crimes including violent crime and domestic violence rose by 8% this year.
He said: "We have already lost 1,100 police officers from the streets of Greater Manchester and this year we are facing another cut of £41m, which [means] there will be hundreds of fewer police officers on our streets.
"To be losing almost half the policing budget by 2020 is unpalatable."
Ian Hanson, chairman of the area's Police Federation, which represents rank-and-file officers, said: "We are in a position where we are going to ask ourselves 'Can we afford the luxury of community policing?'
"In the 1970s and 80s we went to crime after it happened."
He added: "We've got one of the best police forces in the country and now we're under threat and once it's gone, it's gone."
Mr Penning said: "While we acknowledge that the police funding settlement is challenging there is no question that the police will still have the resources to do their important work.
"What matters is how officers are deployed, not how many of them there are in total.
"The reduction in crime nationwide demonstrates there is no simple link between officer numbers and crime levels, the visibility of the police in the community and the quality of service provided."
He said the government has cut red tape and scrapped unnecessary targets.
Greater Manchester Police (GMP) risks "being a reactive force" if up to 400 officers are axed to save £41m next year, the chief constable said.