An investigation by The Sunday Times newspaper focused on a site in the Durham area of northern England.
The report claims that about 10,000 former racing greyhounds have been put down over the past 15 years, simply because they had become too old to compete.
It alleged the animals were killed with a bolt gun - which is legal under current law.
An official at the National Greyhound Racing Club said the inquiry would start immediately.
Anyone connected with the club and found to have been involved would be disciplined, he added.
Animal Welfare Minister Ben Bradshaw said greyhound racing faced losing its right to regulate itself if it did not "clean up its act".
"Greyhound racers should be in no doubt that they are drinking in the last chance saloon as far as self-regulation is concerned," he said.
Government lawyers will study the evidence compiled by The Sunday Times to see if any offences have been committed.
The RSPCA animal charity said the sport needs to act. "This is a huge and totally unnecessary slaughter. There is no justification for killing these animals simply because they can't do their job any more," said a spokesman.
Traditionally a working class preserve, dog-racing has become increasingly upmarket in recent years.
Large greyhound stadiums offer corporate hospitality similar to those at horseracing tracks. About A$3.92 billion a year is bet on the races held on Britain's 31 tracks.
Racing greyhounds, three-quarters of which come from Ireland, can begin to run competitively from 15 months and usually retire before they are seven.
Because the animals have a natural lifespan of up to 12-15 years, many former racers are taken as pets by their owners.
Others are found homes by the Retired Greyhound Trust or are used for breeding.