The attack left 23 dead while a further 43 are missing, city officials said.
Dnipro mayor Borys Filatov said there was "minimal" chance of finding anyone else alive.
Speaking to state TV in Moscow, Russian President Vladimir Putin insisted that military operations were going to plan.
Kyiv, Kharkiv and Odesa were also hit on Saturday in attacks which Moscow said were targeted at Ukraine's military and energy infrastructure.
The devastating strike in Dnipro hit the entrance of a nine-storey building, turning several floors into smouldering rubble.
Mykola Lukashuk, head of the regional council, said emergency services have been able to rescue 38 people.
Around 72 were injured, including 14 children, Mr Lukashuk wrote on Telegram
Rescue teams work in the rubble of the damaged residential building hit by shelling in Dnipro
Speaking on state TV, Mr Putin said "everything is developing within the framework of the plan of the ministry of defence and the general staff".
In his nightly address on Saturday, Ukrainian President Volodymyr Zelensky said debris clearance in Dnipro would continue all night: "We are fighting for every person, every life."
It has been two weeks since the last wave of Russian attacks on Ukraine's power grid. In his address Mr Zelensky said energy infrastructure in the Kharkiv and Kyiv regions had been badly hit.
Following the attacks Ukrainian state energy company Ukrenergo temporarily imposed round-the-clock consumption limits for all regions.
Western and Ukrainian officials have questioned whether Russia's "energy war" might be coming to an end, due to a possible shortage of suitable missiles and the evident fact the strategy has yet to break Ukraine's spirit.
Aftermath of missile strike in Dnipro
Russia's missile barrage came on the same day that UK Prime Minister Rishi Sunak said his government would give Challenger 2 tanks to Kyiv's armed forces in a bid to help "push Russian troops back".
In response, Moscow said providing more weapons to Ukraine would lead to intensified Russian operations and more civilian casualties.