The injury toll was unclear, as broadcaster TV One reported that two civilians, including a female student, had been wounded.
A police bomb squad was investigating the explosion.
Straits Times reported a private-car driver, 17, and student, 19, were among the wounded.
"There were two blasts around 9pm, close to each other, there are three victims," East Jakarta police chief Andry Wibowo told TV station MetroTV. "From the damage I can see the explosions were pretty big."
Witnesses told Straits Times the blasts were 5-10 minutes apart, near a bus stop and a
parking area for motorcycles. Local reports suggested the explosions happened near the terminal's toilet.
TV pictures showed body parts and other debris scattered at the bomb site, smoke rising from the terminal, and police rushing to carry casualties away from the scene.
Large numbers of police officers were at the scene and had cordoned it off.
Witness Sultan Muhammad Firdaus told TV station Kompas TV he heard two explosions about 10 minutes apart.
"The explosions were quite loud, I could hear them clearly," he said. He added he thought two police officers were injured in the blast.
Witness Rohimat told detik.com: "It was at the Kampung Melayu Terminal. Residents panicked and ran. The explosion was very loud." He also said there was a strong smell after the blasts.
Indonesia, the world's most populous Muslim-majority country, has long struggled with Islamic militancy and hundreds of radicals from the Southeast Asian state have flocked to fight with Isis, sparking fears that weakened extremist outfits could get a new lease of life.
A gun and suicide attack in Jakarta killed four attackers and four civilians in January last year, and was the first assault claimed by the Islamic State group in Southeast Asia.
Indonesia has suffered a series of Islamic militant attacks in the past 15 years, including the 2002 Bali bombings that killed 202 people, including Australians.
A sustained crackdown weakened the most dangerous networks but the emergence of IS
has proved a potent new rallying cry for radicals.
The horror explosions come after two men, aged 20 and 23, were caned for having sex with each other in a province on the northern tip of Indonesia's Sumatra island.
It marked the first time the punishment has been handed down for homosexuality since a sharia regulation banning homosexuality in Aceh was introduced in 2014.