The body was taken from the Wharfe at Addingham, near Ilkley in West Yorkshire, by police diving teams who are continuing to search the area.
Lynn and Barry Collett were on honeymoon in the Yorkshire Dales when they went missing last Monday.
A police spokeswoman said it was too early to say whether the body was linked to the couple, but their families, who had returned home after spending last week in North Yorkshire, were travelling back yesterday to identify the body.
"Clearly we cannot confirm whose body we have found at this stage, but given the recent circumstances it is sensible to bring the families back," said the spokeswoman.
Earlier in the week, an estate worker from Bolton Abbey, where the couple were thought to be walking, saw a body in the river, but it disappeared before he could call for help.
Shortly afterwards a red anorak was recovered from the river, which police said had belonged to Mrs Collett, 26. It contained the key to the holiday cottage where the couple, married in Hampshire nine days ago, were honeymooning.
"When we went into the cottage we saw all the presents and a tier of the wedding cake," the spokeswoman said.
"On the day they disappeared there had been heavy rain in the Dales and the river was very high and very fast-flowing. It is a treacherous stretch of water."
Although the police are continuing to search the river and surrounding areas, hopes are fading of finding alive Mr Collett, 29. "It appears to be a terrible human tragedy," said the spokeswoman.Reuse content