Peers approved the move, which will save around £50 million a year from the £200 million annual budget of the Criminal Injury Compensation Board, after hearing that it was necessary to help reduce the deficit.
As a result, around 17,000 victims who suffer "temporary" injuries each year, such as fractured ribs or a dislocated jaw, will lose out on compensation altogether.
Another 13,000 with more serious injuries, including minor brain damage, a fractured skull or damage to the retina, will see their compensation cut. Overall, an estimated 83 per cent of crime victims will lose out.
Labour accused the Government of putting its deficit reduction plan before the needs of the victims of crime.
Speaking in the debate before the vote, Baroness Royall, Labour's leader in the Lords, said: "Victims do not chose to be victims, they have suffered through no fault of their own. The Government is putting deficit reduction before humanity."
A campaign against the cuts is being led by the USDAW trade union, which represents shop workers, who, it is claimed, are often the victims of crime. Lord Davies of Coity, a former general secretary of the union, said: "If this proposal goes through what next ... child labour, then slavery?"
But Lord McNally, a Liberal Democrat Justice Minister, told Labour to "get real" about the state of the economy, and claimed that the changes to the scheme would also bring additional help for some victims.
He said: "The reality that still takes time to sink in apparently across the House is that we are all a lot poorer than we thought we were four years ago.
"It is no use pretending that we are [not] dealing with [taking] relatively small payments for temporary injuries out of a scheme. In return for that we are substantially reforming the amount of money that will go into victim support."
Following vote, the changes are due to come into force in September.
