Adams took over as manager of Norwich, who were relegated from the Premier League last season, on a permanent basis in May after a five-game spell as caretaker boss.
Norwich, who were knocked out of the FA Cup by League One (third tier) side Preston North End in the third round on Saturday, are seventh with 37 points from 24 matches.
"I firmly believe that we are still on course for a crack at promotion back to the Premier League. That is where this club belongs," Adams said in a statement on the Norwich website (www.canaries.co.uk).
"However, I feel it is in the best interests of the team that an immediate change is made in order to ensure a positive impact on results."
The 49-year-old Adams will take a break from the game before returning to Norwich in July in a role yet to be confirmed, the club said.
First team coach Mike Phelan will take charge until a new manager is appointed.
(Reporting by Michael Hann; editing by Ken Ferris)
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