Reverend Tony McSweeney, 66, from Norfolk, was held along with another man aged 70 from East Sussex on suspicion of sexual offences.
The allegations are linked to Elm Guest House and the Grafton Close care home in Barnes, south west London.
A Diocese of East Anglia spokesman confirmed Fr McSweeney was arrested, and said: "The safeguarding of children and vulnerable people is of paramount importance to the Catholic Church and the Diocese is co-operating fully with the police in this investigation."
The arrests were made as part of Operation Fernbridge, which was launched after concerns were raised by MP Tom Watson.
Speaking in Parliament in October last year, he said that a file of evidence used to convict Peter Righton of importing child pornography in 1992 contained "clear intelligence" of a sex abuse gang.
Mr Watson alleged that a member of the group had bragged about links with a senior aide to a former prime minister.
A spokesman for Richmond Council, which ran the care home, said: "Richmond Council considers the safeguarding of all children and young people as an utmost priority and we take any allegations of abuse very seriously. As such we are offering our full support and co-operation to the police during their investigation."
Director of the NSPCC helpline Peter Watt said: "We are assisting the police on Operation Fernbridge and are asking anyone with information to come forward. We will assist the police in gathering evidence and supporting those who come forward."
Commander Peter Spindler from the Metropolitan Police said: "This is a complex multi-agency investigation supported by the NSPCC, Ceop and Richmond Social Services involving non-recent allegations of sexual assault against children. It is vital that anyone who has been affected by or has information about activity in the early 1980s at the Elm Guest House, or the Grafton Close care home, in Barnes speaks to the NSPCC on their helpline on 0808 800 5000, or their local police."
Fr McSweeney has been a priest for almost 28 years.
The 66-year-old trained at St John's seminary near Guildford and is the priest of St George's Catholic Church on Sprowston Road in Norwich.
He was appointed as part-time club chaplain at Norwich City FC in 2003 by Delia Smith and was made a director at Notre Dame High School in Norwich in April last year.