The defeated presidential candidate is also accused of violating military procurement procedures.
He says the charges are politically motivated and an attempt to stop him contesting April's parliamentary polls.
Gen Fonseka was arrested by the army last month. He lost to incumbent President Mahinda Rajapaksa in January.
Protests against his arrest and court martial have been held in Colombo.
Gen Fonseka was in charge of Sri Lanka's army when it defeated the Tamil Tiger rebels last year after 25 years of civil war.
But he and President Rajapaksa fell out over who should take credit for the victory - and both fought the presidential election boasting of their roles in the war.
Officials have also accused Gen Fonseka of plotting a coup and the assassination of President Rajapaksa - charges he denies - but those accusations will not figure at the court martial.
Secret trial
Reporters have been barred from the trial and there is no word yet on Tuesday's proceedings.
The court martial is being held at naval headquarters in the capital, where Gen Fonseka is detained.
There he is being tried, completely in secret, by a panel of officers junior in rank to himself, the BBC's Charles Haviland reports from Colombo.
Even the wording of the charges has not been made public, our correspondent says, adding that sources say some 35 witnesses are likely to be called and that Gen Fonseka could face up to five years in jail.
Gen Fonseka can have his own lawyers present at the court martial and can appeal to the higher civilian courts if he is found guilty, Sri Lanka's military spokesman has told the BBC.
Sri Lanka's ex-chief justice, Sarath Silva, has said the court martial is unconstitutional as Gen Fonseka, in his view, is not subject to military law.
Gen Fonseka would have to be tried in a civilian court, he said.
Gen Fonseka's daughter, Apsara, has accused the government of trying the retired general in order to remove him from the 8 April parliamentary election, in which he intends to stand.
Ahead of the court martial, Gen Fonseka's Democratic National Alliance party said he would not co-operate with the proceedings, AFP news agency reported.
