Commission chief Attahiru Jega said he had been told troops would not be available to help patrol the ballot because they would be fighting Boko Haram militants in the north-east.
Nigeria and four other states plan to deploy a joint force of 8,700 soldiers.
Both the Nigerian opposition and the US criticised the delay.
The head of the party of former military ruler Muhammadu Buhari, who is challenging incumbent President Goodluck Jonathan, said the “provocative” move was a “major setback for Nigerian democracy”.
US Secretary of State John Kerry said the US was “deeply disappointed”, adding: “Political interference with the Independent National Electoral Commission is unacceptable, and it is critical that the government not use security concerns as a pretext for impeding the democratic process.”
The postponement is a highly contentious move, the BBC’s Will Ross reports from Lagos.
Officials from the main opposition party accuse the military of forcing the electoral commission into the delay to help the sitting president’s campaign.
It looks set to be a tight race between Mr Jonathan and Mr Buhari, our correspondent says.
The postponement may well increase the tension which is already palpable, he adds.
Analysis: Will Ross, BBC Nigeria correspondent, Lagos
The delay is highly contentious and will be seen by many Nigerians as foul play. What is not clear at this stage is whether it will favour President Goodluck Jonathan or his rival, Muhammadu Buhari.
Attahiru Jega made a point of saying this was a decision taken by the electoral commission but clearly the “referee” was under intense pressure.
The Boko Haram conflict has raged for five years but just days before the vote Professor Jega was suddenly told the entire military would be focused solely on the north-east – in other words, “you are getting no help from the military, you are on your own”. With the threat of violence so real, he was put in a tight corner.
But it seems highly unlikely that the conflict will be brought to an end within the next few weeks so will the election be held at all? That may depend on whether some powerful personalities feel President Jonathan is well placed for a victory.
‘Onerous responsibility’
“The commission cannot lightly wave off the advice of the nation’s security chiefs,” said Mr Jega.
“The risk of deploying young men and women and calling people to exercise their democratic rights in a situation where their security cannot be guaranteed is a most onerous responsibility.”
Parliamentary elections due to take place on 14 February have also been postponed to 28 March.
Elections for state governors and assemblies slated for 28 February have been moved to 11 April.
John Odigie-Oyegun, chairman of Mr Buhari’s All Progressives Congress, said: “I strongly appeal to all Nigerians to remain calm and deist from violence and any activity which will compound this unfortunate development.”
