The three-judges said they wanted to clarify whether they could conduct both sets of proceedings, a defense lawyer told the BBC.
Wednesday's trial was to have heard charges that Gen Fonseka broke procedure on military procurement.
Gen Fonseka says all the charges are politically motivated and an attempt to bar him from forthcoming elections.
He was arrested by the army last month, after losing presidential elections to incumbent Mahinda Rajapaksa in January.
Gen Fonseka led Sri Lanka's army when it defeated Tamil Tiger rebels last year but he and President Rajapaksa later fell out.
On Tuesday the general appeared before the court on charges of participating in politics while in uniform.
The trial was adjourned to 6 April after defense objections. Wednesday's hearing was adjourned indefinitely.
The army said the tribunal wanted to be reconvened to ensure transparency and a lack of prejudice.
A spokesman for the general said it was a delaying tactic aimed at preventing him from campaigning for 8 April general elections.
"The army judges did not wake up this morning and discover that they have been appointed to both courts," the spokesman, Anura Kumara Dissanayake, said. "They knew it from the day they were appointed."
Separately, two other cases are pending at the Court of Appeal and the Supreme Court, both petitioning for the general's release.