He took office on July 20 but will be taking a break from his day-to-day duties to spend time with his family.
He will remain in direct contact with officials and continue holding meetings during the overseas break, with allies insisting the government will continue functioning normally during his absence from Downing Street.
Burnham, who is married with three children, has made a blizzard of announcements during his first fortnight in No 10.
His holiday comes after his campaign to win the Makerfield by-election in June led to a rapid rise to replacing Sir Keir Starmer.
Officials would not be drawn on where the prime minister is holidaying, although it is understood to be abroad rather than within the UK.
His most recent public appearance was on Sunday in Dover, a popular port for ferry crossings to the continent, although he was using the visit to Kent to promote his government's efforts to tackle small boat crossings.
Reform UK chairman Lee Anderson criticised the prime minister, saying: "Two weeks into the job and Andy Burnham has already had enough.
"After dropping a number of unfunded commitments and overseeing over 2000 illegal migrants breaking into our country he's bunked off for a jolly abroad.
"This isn't a prime minister that's serious about leading."
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