Derbyshire Police said they were not looking for anyone else in connection with the deaths but did not immediately reveal what the man had been arrested on suspicion of.
The force discovered the bodies after being called to an address on Chandos Crescent in Killamarsh, near Sheffield, at around 7.25am on Sunday.
Close family of the victims have been informed and are being supported by specially trained officers.
One local told Yorkshire Live: “It’s a bit of a shock, it’s usually quiet round here so you don’t usually see police, not like this anyway.
Another added: “We’ve been away for 10 days and thought ‘oh god’ when I saw all of this.
“Police said ‘don’t worry’ to us but we don’t know anything.”
DCI Rob Routledge, who is leading the investigation, said: “We would really like to hear from anyone who saw or heard anything suspicious in the early hours of this morning, or has any information which they think could help with our inquiries.
“No matter how small you think that information may be, please do get in touch with us.
“It is understandably a worrying time for the community, and we would like to thank them for their patience and understanding at this time.
“It was important to us that close relatives of those involved were informed before we could give further details about incident.
“Residents will continue to see a large police presence in the area, and patrols are being carried out for reassurance.
“If you do have any concerns, please don’t hesitate to speak to them.”
Police have urged anyone with information about the incident to come forward.
North East Derbyshire MP Lee Rowley offered his condolences following the “terrible and hugely tragic” incident.
“Terrible and hugely tragic news from Killamarsh this evening. Our condolences to the family and our thoughts are with them,” Mr Rowley said on Twitter.
The Tory MP also paid tribute to Killamarsh as a “lovely” community” which would show its resilience “at this difficult time”.
“Killamarsh is such a lovely, close knit and warm community and I know that many residents will be shocked & worried by the news,” he tweeted.
“This is believed to be an isolated incident with an arrest having been made. I’ve no doubt that the village will pull together at this difficult time.”