President Viktor Yanukovych vowed to investigate and punish the perpetrators.
"This is yet another challenge for us, for the whole country," Yanukovych told reporters in televised comments. "We will think of how to respond to this properly."
The opposition party led by the jailed former prime minister, Yulia Tymoshenko, however, suggested that Yanukovych's government may have organized the blasts in order to deflect the world's attention from Tymoshenko's imprisonment and reported abuse in prison.
The president's office declined to comment on the opposition charges. But Prime Minister Mykola Azarov commented on his Facebook page that the blasts "are profitable to those forces that are interested in destabilizing the situation in the country."
The first of four explosions rocked a tram stop shortly before noon, injuring 13 people, said Emergency Situations Ministry spokeswoman Yulia Yershova. The bomb was planted in a garbage bin.
The second bomb, also planted in a garbage bin, went off about 40 minutes later near a movie theater and a trade school, injuring two adults and nine teenagers. A third blast in the city center wounded three people and a fourth, also downtown, caused no casualties.
Television footage showed passers-by walking among broken glass trying to help a moaning victim of the tram-stop explosion, while others bandaged a bloodied arm of another victim, a middle-aged man. An elderly woman with blood on her legs lay motionless on the ground and pleaded with someone to call her daughter. Other victims were put on stretchers and transported into ambulances.
"It's painful that such a thing can happen in broad daylight," one unidentified middle-aged woman from Dnipropetrovsk told Channel 5 television in a trembling voice.
Deputy parliament speaker Mykola Tomenko, who is member of Tymoshenko's party, suggested the blasts were orchestrated by the government in order to quiet Western criticism of the Tymoshenko case.
"I don't rule out that the authorities and law enforcement bodies may be among the organizers of a scenario, which involves deflecting the attention of the world and Ukraine form Tymoshenko's case on the whole and her beating in particular," Tomenko said in a statement.
Tymoshenko, 51, the country's top opposition leader, is serving a seven-year prison term on charges of abuse of office in a case harshly criticized by the West as politically motivated.
She and Yanukovych are bitter rivals. Tymoshenko came to power amid the 2004 Orange Revolution when Yanukovych's fraud-tainted win as president was thrown out. He then beat her in Ukraine's latest presidential vote in 2010.
Tymoshenko has been on a hunger strike for a week to protest the alleged prison abuse. She claims guards punched her in the stomach and twisted her arms and legs while transporting her to a local hospital against her will to be treated for a spinal condition.
Prison officials deny mistreating Tymoshenko. But photos taken by Ukraine's top human rights official, Nina Karpachova, of Tymoshenko in bed in her jail cell show splotches on her abdomen and lower arm.
Tymoshenko's daughter Eugenia said Friday that her mother is very weak after refusing food for seven days and fears that she will be force-fed by prison officials.
The European Union has expressed alarm over the investigation and Germany has pressed Ukraine to urgently treat Tymoshenko and investigate the beating allegations.
German President Joachim Gauck this week canceled a visit to Ukraine next month, and calls are growing for EU government officials to boycott the Euro 2012 soccer championship that Ukraine will co-host with Poland in June.
In a previous attack in January 2011, two pre-dawn explosions outside a coal mining office and a shopping center in the Ukrainian city of Makiyivka caused no casualties. Authorities then received letters demanding money in exchange for an end to the blasts. The perpetrators were arrested and sentenced to lengthy prison terms.