But education officials are concerned that schools in Rift Valley, worst hit by the violence, may not resume lessons due to a lack of students and teachers.
Tension remains high as the opposition Orange Democratic Movement prepares to begin three days of anti-government demonstrations on Wednesday.
Some 600 people were killed and 250,000 displaced during the clashes.
ODM leader Raila Odinga says he was robbed of victory and says President Mwai Kibaki should stand down.
Over the weekend, the East Africa Community observer mission said Kenya's election had fallen short of being free and fair.
Security in these areas is still unstable and we have asked our members not to risk [it]
Njau Kuria
Kenya National Union of Teachers
The observers' report says the presidential vote tallying was grossly mismanaged and critically undermined the credibility of the final stage of the electoral process.
Former UN Secretary-General Kofi Annan is expected to begin mediation efforts this week, aimed at ending the political impasse between the two men.
Mr Annan heads a panel set up by the African Union, which includes former Tanzanian President Benjamin Mkapa and Nelson Mandela's wife Graca Machel.
The government has banned the ODM rallies, raising fears of clashes between police and the protesters.
Parliament is due to reconvene on Tuesday - another possible flashpoint.
The ODM and its allies won a majority in parliament but they may refuse to swear an oath of allegiance to the president.
Colleges closed
In Nairobi, most primary and secondary schools re-opened as directed by the ministry of education.
The city's customary traffic jams have resumed as business returned to normal.
Children walking through traffic jams
Nairobi's children have to negotiate the traffic jams which have returned
Parents in most parts of the country rushed to shops over the weekend to buy uniforms and other school materials for students.
But some universities and government-run colleges, which were also scheduled to begin academic programmes, have remained closed and have advised students to remain at home until further notice.
In Rift Valley, the Kenya National Union of Teachers estimates that some 400 teachers were displaced during the post-election violence.
The most affected areas are Kuresoi, Njoro, Uasin, Gishu and Molo, where the union says at least 30 schools may not re-open.
"Security in these areas is still unstable and we have asked our members not to risk [it]," said KNUT secretary Njau Kuria.
"Some schools are also hosting displaced people and therefore cannot operate," he said.
In Kisumu, another area hit by violence, the BBC's Muliro Telewa says many schools have re-opened but not many students or teachers have turned up, due to lack of transport and security fears.
Source: BBC
