Siasia was dismissed after a meeting of the Nigerian Football Federation (NFF) on Friday, before his removal was confirmed by officials a day later.
His sacking follows the departures of Javier Clemente at Cameroon and Tom Saintfiet from the Ethiopia post in the last seven days.
The 44-year-old, who played for Nigeria at the 1994 World Cup and later coached the country's under-23 team to the silver medal at the 2008 Beijing Olympics, was fired after Nigeria's shock failure to qualify for next year's finals.
Nigeria finished runners-up in their group after failing to beat Guinea at home in their decisive group game earlier this month.
A statement said Siasia and his assistants "breached a key proviso in their contract with the NFF and their services are therefore promptly dispensed with," a reference to the minimum requirement of qualifying for the Nations Cup.
A successor would be discussed next week, officials said.
Former Spain manager Clemente was fired by Cameroon on Monday after they too, missed out on the Nations Cup, being co-hosted by Equatorial Guinea and Gabon from January 21 to February 12.
Belgian coach Tom Saintfiet said on Friday he was leaving his job as Ethiopia coach after just five months, citing broken promises for his departure.
"Despite the many positives, some agreements were not honoured and that is the reason for this decision," he said in an e-mail to Reuters.
Saintfiet had been in charge for three Nations Cup qualifiers since June, including a 2-2 draw with Nigeria that contributed to the Super Eagles missing out on the finals.
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