Mr Blunt said the justice system could cope in the short-term and there would be no long-term effect on the prison population in England and Wales.
Last Friday the number of inmates hit a record of almost 87,000, largely driven by the riots, but the government expects numbers to fall again in 2012.
Mr Blunt was speaking at the launch of a tougher community service regime.
BBC home affairs correspondent Danny Shaw said Mr Blunt believed harsher terms for rioters were justified under case law.
But the coalition's long-term plan to reform prisons and sentencing was unaffected by the riots, our correspondent added.
Ministers have said they want to cut costs by reducing the population through the introduction of the more robust community sentences for some offenders and improvements in the rehabilitation of offenders.Adequate punishment?
Since the riots, the prison population has gone up by more than 1,000.
As of Tuesday, there were 797 suspects on remand, almost two-thirds of all those to have so far come before the courts.
Prisons chiefs have devised contingency plans in case they run out of space.
In his first interview since the disturbances, the prisons minister said that he was completely confident the system could cope and that the jail population would be back to where it was before the trouble within six months.
"We are completely confident that the prison system and justice system are going to be able to cope with what the police are producing for us," he told the BBC.
"This is an exceptional event. There will be a one-off increase in prison numbers as people serve their sentences.
"What we have to do is make sure there are prison places for those sent to prison by the courts and we will continue to do that regardless of how many people are sent to prison."
His comments came as he promoted the Ministry of Justice's previously-announced plan to make more use of community-based sentences for some offenders.
Mr Blunt confirmed that from next year unemployed offenders doing unpaid work - known as community payback - will be made to do it full-time rather than spread out over many months.
Under the current arrangements, offenders can work as little as six hours a week on manual labour projects such as cleaning up graffiti.
The scheme aims to force offenders to work a minimum of 28 hours over four days with the fifth spent looking for a job. Ministers say the punishment will also be delivered more immediately after sentence.
Some 100,000 offenders are given community sentences every year and the public can nominate online the jobs they want doing.
Labour said "tough community sentences" were appropriate in some circumstances but questioned how the government's plans could be achieved under planned cuts to probation services.
A spokesman said: "People will want assurances that sentences being served by offenders in the community are providing adequate punishment as well as rehabilitation and that they are being carried out safely with proper supervision."
Harry Fletcher, assistant general secretary of probation union Napo, said: "Previous attempts to have offenders doing payback all week have failed because they would have lost their Jobseeker's Allowance as they would have been unavailable to seek work.
"This proposal gets round that problem; however, the scheme will only be viable if it is properly resourced, if it doesn't put council workers out of work and that the offenders are fit to carry out the tasks."
Paul McDowell, from the crime reduction charity Nacro, said the "proposals must strike the right balance between punishment and public protection".