Italian media say two families were living in the four-storey building that collapsed in Torre Annunziata district. Two children are among those missing.
The cause remains unclear. Neighbours did not report hearing any explosion - just the crash of masonry at dawn.
Some masonry fell on the nearby Naples-Salerno railway line, so traffic on it has been suspended.
It is a seismically active area but there is no suggestion that an earth tremor jolted the building.
There are suspicions that the collapse could be linked to vibrations from the railway, or to renovation work that was under way on the lower floors.

Ambulance staff were called to Woodgate Gardens, Bartley Green, in Birmingham, at about 22:50 BST on Monday, West Midlands Police said.
The man was taken to hospital and died shortly after, a police spokesman said.
The two have been arrested on suspicion of murder following the death of the 22-year-old man, and remain in custody, police said.
See more stories from across Birmingham and the Black Country here
The area was cordoned off for forensic investigations and CCTV of the surrounding area is also being examined.
Det Insp Harry Harrison said: "We are making real progress in the investigation, I'd like to thank the community for their continued support and ask that anyone who has any information who hasn't yet come forward gets in touch as soon as possible."

Seven riders in the peloton crossed with the safety barrier down, but were not sanctioned for breaking race rules.
Sir Bradley Wiggins finished 18th in his final race for Team Sky, 31 seconds behind German winner John Degenkolb.
"It's the most beautiful race in the world and we get bothered by a train," said French champion Arnaud Demare.
"This needs to be taken care of, it was dangerous. We went through but it was close."
One rider from the Belgian Lotto team was clipped by a barrier which came down seconds before the 60kph train sped past.
Race organisers said the peloton were 10m from the barrier as it started to descend and that the leading riders "could not stop in safe conditions".
A police motorcycle stopped the rest of the pack, before organisers of the 151-mile race slowed the leaders to allow the pack to catch up.
Former British champion and Olympic track medallist Rob Hayles, commentating on BBC Radio 5 live sports extra, said: "That could have ended in disaster.
"You could see riders nip across but that train wasn't slowing down."
A similar incident occurred last year but it affected only the eight men in the breakaway.
In 2006, three riders who were chasing a lone breakaway by eventual winner Fabian Cancellara were disqualified after crossing a railway line after the barrier was down.

The 20-year-old follows Danny Ward from Anfield to the Scottish Premiership, the goalkeeper having been with the Dons since the start of the season.
Aberdeen manager Derek McInnes told the club website: "He's a player who has always impressed us and will give us good options in the months ahead."
The Northern Ireland international joined Liverpool from Glenavon aged 16.
He has yet to make his competitive debut for the Premier League side but made nine appearances while on loan to Barnsley in the Championship in the second half of the 2013-14 season.
That led to the first of three international caps and his only senior appearance last season was in a 1-0 friendly defeat by Scotland.
"Ryan has the quality needed to play with us at Aberdeen and we are looking forward to working closely with him," added McInnes.
"Ryan's eagerness to join us over others also give us great encouragement."
McLaughlin's older brother, Conor, is also a right-back, with League One club Fleetwood Town, and has six Northern Ireland caps.
Rescuers in southern Italy are trying to find eight people missing after an apartment block collapsed in Naples.
[NEXT_CONCEPT]
A 16-year-old boy and 21-year-old man have been arrested after a man was fatally stabbed.
[NEXT_CONCEPT]
Several Paris-Roubaix riders were seconds from being hit by a train as they raced over a rail crossing while a TGV approached.
[NEXT_CONCEPT]
Liverpool right-back Ryan McLaughlin has joined Aberdeen on loan until January.