The soldier's family told the Manchester Evening News they were ''devastated'' by his death. It is understood his father has already flown out to the Mediterranean island.
Mr Collins was off-duty with three other soldiers when they became involved in a brawl with three British holidaymakers in the early hours of yesterday morning.
One of the tourists allegedly stabbed the soldier with a knife, according to police spokesman Georgios Economou.
A spokesman for the Ministry of Defence (MoD) said yesterday: ''It is with great sadness that the MoD must confirm that a soldier from 2nd Battalion The Royal Regiment of Fusiliers has died in an incident in Cyprus.
''An investigation is being conducted by Cyprus police and it would be inappropriate to comment any further. The family has been informed and our thoughts are with them.''
Mr Collin's battalion was due to leave for Afghanistan on Saturday but the mission was delayed for 24 hours, according to reports.
Two of the suspects are reportedly of Pakistani origin and one of Somali origin.
A Foreign and Commonwealth spokesman said: ''We are aware of the arrest of three British nationals in Ayia Napa and we are providing consular assistance.''
Tributes have been paid to Mr Collins on Twitter while a Facebook page has been set up in his memory.
One Twitter user wrote: ''Gutted to hear the death of an ex-army cadet and soldier, RIP David Collins, good memories from Camp 2010.''
Another added: ''Rest In Peace David Collins, You Was A Perfect Solider, Sleep Tight!''
Connie Pierce, a British military spokeswoman, said the attack took place in an area of the Eastern Mediterranean island that British soldiers are told to avoid because of previous incidents.
After the rape and murder of Danish tour guide Louise Jensen by British servicemen in 1994, the centre of Ayia Napa was declared off limits to soldiers by military top brass on the island, which is a clubbing resort with a reputation for sex, drugs and violence.
About 3,000 British military personnel are stationed in Cyprus at bases retained after the former British colony gained independence in 1960.
In 2008 nine British soldiers went on trial accused of trashing a pub and beating up its owner during a mass bar brawl on the island.
The servicemen, who were celebrating finishing tours of Iraq and Afghanistan and coming home to the UK, were all acquitted.