The first two blasts happened at a busy central tram stop and near a local cinema, officials said.
All the devices were apparently planted in rubbish bins.
No suspects have been identified yet and such an attack is unusual for Dnipropetrovsk. The industrial city is the birthplace of jailed opposition leader Yulia Tymoshenko.
“This is yet another challenge for us, for the entire nation,” President Viktor Yanukovych said.
Nine children were among the 27 injured in the blasts, which all happened within an hour.
Tensions are running high over the alleged mistreatment of Ms Tymoshenko. She was a leader of the pro-Western Orange Revolution in 2004 but her chief rival, Mr Yanukovych, won an election in 2010 and forged closer ties with Russia.
Ukraine is also preparing to co-host the Euro 2012 football tournament this summer.