Rovers are currently at the bottom of the League Two table after losing seven of their opening 12 games.
The 41-year-old Welshman, who retired from playing in 2011, joined Tranmere back in May.
"Rob is a decent man who has worked very hard over the past few months for the football club," chairman Mark Palios told the club's official website. "However, with the club currently sitting at the bottom of League Two for the first time in 32 years it was decided this was the right time to make the break."
Tranmere continue their league campaign on Saturday when they make the trip to Oxford United.