Regional leaders have been unsuccessfully trying to persuade him to hand over power to Adama Barrow, who won December’s elections.
The move comes after Nigeria deployed a warship to put further pressure on Mr Jammeh.
Regional bloc Ecowas has prepared a force but maintains that military intervention would be a last resort.
In his televised announcement, Mr Jammeh said “any acts of disobedience to the laws The Gambia, incitement of violence and acts intended to disturb public order and peace” are banned under the state of emergency.
He said security forces were instructed to “maintain absolute peace, law and order” and denounced foreign interference in The Gambia’s election.
Mr Barrow, a property developer, is meant to be inaugurated as the new president on Thursday.
Mr Jammeh initially accepted the election results but then decided he wanted them annulled after the electoral commission admitted some errors, although it insists this did not affect the final outcome.
The Supreme Court is unable to hear the challenge until May because of a shortage of judges, and Mr Jammeh has said he will not step down until then.
At least three Gambian ministers, including the foreign minister, have resigned in recent days. Thousands of Gambians have also fled to Senegal, and further afield to Guinea-Bissau, amid fears of violence.
Map of The Gambia
BBC Africa security correspondent Tomi Oladipo says the Nigerian warship is being deployed to put on a show of strength rather than to launch an attack.
A military source says that the vessel – the NNS Unity – is currently sailing off the coast of Ghana.
Mr Barrow won 43.3% of the vote compared with Mr Jammeh’s 39.6%. A third candidate, Mama Kandeh, got 17.1%.
Yahya Jammeh seized power in the tiny West African country in 1994 and has been accused of human rights abuses, although he has held regular elections.
The African Union has said it will no longer recognise Mr Jammeh’s authority after his term ends. Mr Barrow is currently in Senegal.
He was unable to attend the funeral of his eight-year-old son on Monday due to security fears. The boy was mauled by a dog.