The Leyton Orient defender, who used to play for Liverpool, was held in Brompton Road, Knightsbridge, on Tuesday, the BBC understands.
The Met Police said a 33-year-old man and a 31-year-old woman were arrested and taken to a west London police station.
They have been bailed until late April.
In a statement, Leyton Orient Football Club said: "The club are aware of the incident reported earlier today involving Andrea Dossena."
It added it would not comment further whilst it was being dealt with by the authorities.
Dossena scored against Manchester United and Real Madrid while he was at Liverpool.
After joining Liverpool for £7m in July 2008, Dossena scored in the Reds' 4-0 win against Real Madrid in the Champions League in March 2009 and then again in the club's 4-1 away victory at Old Trafford against Manchester United.
The Italian, who won 10 caps, joined Napoli in January 2010 before a spell at Sunderland in 2013-14.
He joined League One Leyton Orient in November last year.

The office building had been owned by the Royal London Mutual Insurance Society but was put on the market for £40m in October.
The Grade I listed property has the two famous Liver Birds on its roof.
Along with the Cunard and Port of Liverpool Buildings, it is one of the Three Graces on the city's waterfront.
The 330,000 sq ft (31,000 sq m) building is currently home to companies including ITV and HSBC.
Thomas Landschreiber, chief investment officer of Corestate, said the company is looking to "invest significant funds to maintain and strengthen this city-building office building in the long term".
"As a new owner of this emblematic building, we appreciate its heritage and its importance to the people of Liverpool," he added.
Source: Museum of Liverpool

Sheffield Wednesday's Chris Kirkland, 31, required treatment after being struck in the face during Friday's game against Leeds United at Hillsborough.
Leeds fan Aaron Cawley, 21, from Cheltenham, Gloucestershire, pleaded guilty at Sheffield Magistrates' Court to assault and entering the field.
He was given a 16-week jail sentence and a six-year football banning order.
Leeds United said the club intended to ban him from its Elland Road stadium for life.
Kirkland, who has played once for England, was shoved in the face and fell to the ground moments after conceding an equaliser in the 76th minute of the match at Hillsborough, which finished in a 1-1 draw.
The court was told that Kirkland made a victim impact statement which said: "I feel shocked, upset and angry.
"I think the man is a thug and should be caught and put in jail. Anyone who supports what he's done is just as bad."
The court heard Cawley had been drinking heavily and had already breached two previous banning orders.
Prosecutor Paul Macauley said Cawley told police he had drunk a number of cans of lager and three-quarters of a litre of vodka before arriving in Sheffield and then had a further seven to 10 pints of cider.
Mr Macauley said he was "so drunk" he did not remember what happened, and only realised after seeing the footage.
District Judge Redhouse heard that Cawley emailed the police to say sorry and also emailed Sky Sports, which broadcast the match, in the hope his apology would be passed on to the two clubs and Kirkland.
A spokesman for Leeds United said: "We are pleased to see the matter dealt with by the courts so quickly.
"The club will also ban the individual for life from Elland Road when this banning order expires.
"While we are pleased to see justice brought so quickly, our one disappointment is that we feel the sentence could, and should, have been considerably longer."
Writing on Twitter, Angela Smith, the Labour MP for Penistone and Stockbridge, also criticised the sentence.
The MP, a Sheffield Wednesday fan, wrote: "16wks prison sentence for assaulting a goalkeeper & breaching a banning order? I am quite frankly astonished! #justicenotdone."
Ex-Premier League footballer Andrea Dossena has been arrested on suspicion of shoplifting at London department store Harrods, the BBC has learned.
[NEXT_CONCEPT]
Liverpool's iconic Royal Liver Building has been sold for £48m to Luxembourg-based real estate investment manager Corestate Capital Holding.
[NEXT_CONCEPT]
A man has been jailed for running on to the pitch and attacking a goalkeeper during a Championship football match.