The bride, who was still wearing her wedding dress, was accused of shouting racist abuse at the guards, who were Asian.
The groom was arrested on suspicion of assault while his wife was held on suspicion of a racially aggravated public order offence.
They were taken to the local police station, where they spent the night in separate cells.
Nick Adderley, Chief Superintendent of Greater Manchester Police's North Division said his officers made the right decision.
Speaking to the Manchester Evening News, he said: "Police officers were asked attend and we did so.
"But it absolutely was and I support the officers who made that decision.
"We can't have a situation where, regardless of what ceremony they have been to, people are being allegedly assaulted and racially abused."
Serena Williams crashes wedding in her swimsuit on Miami Beach
Cheeky whale photobombs couple's wedding picture
Hotel wedding venue owner calls couples 'chavs' after price rise complaints