The bombings began around noon and targeted a tram stop, a theater and a railway station, RIA Novosti reported.
Authorities said there were at least four blasts. Others reported as many as10.
Investigators treated the attacks as acts terrorism, Britain's Guardian reported.
Ukraine has no recent history of terrorism and it was unclear who was responsible for the attacks, the report said.
"We don't know why this would have happened," said Chris Cole, a 22-year-old English teacher from Swindon, England, who lives in Dnepropetrovsk. "It's dead outside -- all you can see is police officers and medics. I've never heard the city so quiet."
Emergencies Ministry officials said the bomb at the tram stop was hidden in a garbage bin. The blast destroyed the facility and damaged vehicles parked nearby, Ukrainian online media publication ForUm reported.
About an hour later, a second bomb went off at the theater, emergency personnel said. It, too, was hidden in a garbage bin.
A third explosion occurred near a railway terminal and a fourth in a public park, RIA Novosti reported.
"We understand that this is yet another challenge for us, for the entire nation, Ukrainian President Viktor Yanukovych said.
Kate Moss Playboy shoot is classic Playboy, classic Kate
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie