where more than 200 schoolgirls were abducted, officials say.
Sources had told the BBC he would stop in Chibok, in the north-east, on his way to a conference in France on the threat from Boko Haram militants.
But the visit was called off for security reasons, the officials said.
The president - under pressure over his government's failure to rescue the girls - will fly direct to Paris.
The BBC's Gabriel Gatehouse in Nigeria says the cancellation of this visit underlines just how fragile the security situation is in the north-east.
On Thursday, relatives of the girls called for their unconditional release by Boko Haram.
Mr Jonathan is said to have ruled out negotiations over a possible release of prisoners.
Nothing was seen of the girls for almost a month after they were taken from Chibok.
But on Monday the group released a video showing more than 100 of them and offering an exchange for prisoners.
UK Africa Minister Mark Simmonds said Mr Jonathan had "made it very clear that there will be no negotiation" at a meeting on Wednesday.
President Jonathan has been criticised for not visiting the town - more than a month after the girls were seized.
The president will travel to Paris to take part in a summit convened by French President Francois Hollande to discuss Boko Haram.
The leaders of Nigeria's neighbours - Benin, Cameroon, Niger and Chad - are scheduled to attend the summit on Saturday, which will also include representatives from the UK, US and EU.
A statement said delegates at the meeting will "discuss fresh strategies for dealing with the security threat posed by Boko Haram and other terrorist groups in west and Central Africa".
'Troubling atrocities'Meanwhile, US officials on Thursday criticised the speed of Nigeria's response to the threat from Boko Haram.
Alice Friend, director for African affairs at the US defence department, said its security forces had been "slow to adapt with new strategies and new tactics".
John Simpson assesses the threat of Boko Haram
She also said the US was unable to offer aid to Nigeria's military because of "troubling" atrocities perpetrated by some units during operations against Boko Haram.
"We cannot ignore that Nigeria can be an extremely challenging partner to work with," Ms Friend said.
State of emergencyUS drones and surveillance aircraft have been deployed to assist in the search for the schoolgirls, while the UK has sent a military team to the capital, Abuja, to work alongside US, French and Israeli experts.
The lower house of Nigeria's parliament, the House of Representatives, approved an extension of the state of emergency in the north-east states of Yobe, Borno and Adamawa on Thursday.
President Jonathan had requested a six-month extension, calling the security situation in the region "daunting" and saying he was concerned by the mounting loss of life among civilians.
The state of emergency, which still needs to be approved by the Senate, gives the military widespread powers such as detaining suspects, imposing curfews and setting up roadblocks.
On Thursday, there were reports of fresh attacks by suspected Boko Haram militants in Borno state.
A witness told the BBC's Hausa Service that there had been explosions in Gamboru Ngala, were some 300 people were killed last week in a massacre blamed on Boko Haram.
reate an Islamic state in northern Nigeria. 
