"The rescue operation is continuing and of course it is possible that people are still beneath the rubble," a spokesman for the ministry said.
Ukraine's Kanal 5 television reported that there were fears of more than 20 dead.
The ministry's website said six of the 23 injured were children, with a total of 70 people rescued from their apartments.
The local gas utility in Dnipropetrovsk said the explosion was caused by a sudden increase in gas flows to the area.
However, some residents observed three men behaving suspiciously near the building's gas supply earlier in the day. Witnesses said that the three arrived at the building in a black car and played with the gas supply shortly before the explosion.
Ganna, a local resident, said: "Three men in leather jackets got out [of the car]. They headed for the trap door [of the gas system]."
"They did something and left quickly. The explosion happened after they left."
Several people said they could smell gas beforehand.
Local televsion showed residents climbing down ladders and escorted by firefighters against a background of twisted window frames and cracked concrete.
Window panes were shattered and a large pile of mangled rubble lay at the base of the building.
Meanwhile, Viktor Yushchenko, the president, ordered Viktor Yanukovich, the prime minister, to deal with the aftermath of the blast and determine its origin.
Prosecutors have opened a criminal investigation into the causes of the accident.