Weiss steps down as Slovakia coach
"Failure to qualify is the simple reason why we came to an agreement about ending his tenure," SFZ President Jan Kovacik was quoted as saying on uefa.com.
"If the team had better results, we would have no reason to change," said Kovacik, though he added: "To be honest, I think he will come back one day."
Weiss led the team into the last 16 at their maiden World Cup in 2010, helped by a win over 2006 champions Italy, but the team finished fourth in qualifying Group B for Euro 2012.
Kovacik said it had not yet been decided who would take over as national coach.
Weiss, 47, will continue his job as coach of Slovan Bratislava.
"We will remember fantastic days during the World Cup finals in South Africa forever," Slovakian captain Marek Hamsik was quoted as saying by Slovak agency SITA.
"Coach Weiss knew how to squeeze the maximum possible out of us, he has done everything in his powers for the national team."