Police said the arrested man, 30, was also suspected of two assault offences.
PC Neil Doyle, 36, was attacked near the Aloha Club in the city centre early on Friday and died of bleeding around the brain.
A 28-year-old suspect handed himself in earlier. The suspects, both from Huyton in Merseyside, are being interviewed by detectives.
Merseyside Police has been granted permission to keep the 28-year-old in custody for further questioning until Monday night.
Officers said the 30-year-old suspect had been arrested on suspicion of murder and "two offences of Section 18 assault" - causing grievous bodily harm with intent.
PC Doyle was with two colleagues when they were assaulted on Colquitt Street, during a Christmas night out.
A post-mortem examination revealed major blood vessels were damaged, and police said his injury was consistent with an assault.
Investigators are considering the possibility that the three men were attacked after being recognised as police officers, although a Merseyside Police spokesman stressed it was "not a set-in-stone motive".
Chief Constable Sir Jon Murphy said the off-duty officers had been subjected to "an apparently unprovoked attack by a group of males".
"Following intensive emergency treatment at the scene Constable Doyle was taken to Royal Liverpool Hospital, where he sadly died a short time later," he said.
PC Doyle had been due to go on honeymoon with his wife Sarah, next month.
In a statement she said: "Neil was very well loved by all of his family, friends and colleagues and it is a great loss to us all.
"We are finding it extremely difficult to come to terms with what has happened and need time to be left to grieve."
Merseyside Police Federation chairman Peter Singleton said PC Doyle was "a good cop that any officer would be proud to call a colleague".
A second man has been arrested on suspicion of murdering an off-duty police constable in Liverpool.