The England captain was pictured in the Sun newspaper looking worse for wear having dropped in on a wedding party over the weekend following Friday's victory over Scotland at Wembley.
"Naturally Wayne is sorry that pictures taken with fans have been published today,” the statement said.
“Although it was a day off for the whole squad and staff, he fully recognises that the images are inappropriate for someone in his position.
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“Earlier today Wayne spoke privately to both Gareth Southgate and (FA technical director) Dan Ashworth to unreservedly apologise. He would like to further extend that apology to any young fans who have seen these pictures.”
Manchester United forward Rooney had started England's 3-0 victory over Scotland, but withdrew from the squad ahead of Tuesday's 2-2 draw with Spain due to a minor knee injury.
The English Football Association have said they will now review what players are allowed to do in their free time.
“All England personnel have a responsibility to behave appropriately at all times. We will be reviewing our policy around free time whilst on international duty,” the FA said in a statement.
A report on Sky Sports said that Rooney's club manager, Jose Mourinho, was angry that the forward had been with members of England's backroom staff into the early hours of Sunday.
The report added that Rooney, who has endured a difficult season and found himself on the bench for both club and country, will be assessed by United’s medical staff ahead of Saturday’s Premier League home game against Arsenal.
(Reporting by Toby Davis; editing by Pritha Sarkar)
