Suker, Croatia's record goalscorer, has headed the HNS since 2012.
He has been replaced by HNS executive director, Marijan Kustic, who was the only candidate for the post.
"I'm glad that I was part of Croatia's football biggest successes both as a player and HNS president", Suker said.
The 53-year-old former Real Madrid striker played for Croatia when they finished third at the 1998 World Cup in France.
The reasons for his departure were not clear but the media speculated that Suker was insufficiently dealing with problems that Croatia football is facing, notably poor infrastructure.
Earlier this week, a local television station broadcast a recording of an alleged phone conversation between fugitive football strongman Zdravko Mamic, sentenced to jail over a multi-million-euro graft, and a former HNS official.
"You should start changing relations within the federation, Suker can no longer be president, end of story," Mamic, hiding in neighbouring Bosnia, can be heard as saying to Zorislav Srebric.
The latter confirmed to Nova TV that he had phone conversations with the former Dinamo Zagreb boss to "analyse matches" without elaborating when they took place.
Suker declined to comment.