Planet Earth will be available free with an "imminent" edition of the paper before it launches anywhere else in the world. The 10-track CD will then go on sale on July 24.
HMV denied that it would not be stocking the album, but said it was "disappointed in the move" because it "devalues music". Before the speculation was confirmed, Simon Fox, HMV chief executive, said that he thought the move would be "absolutely nuts".
The Entertainment Retailers Association said the giveaway "beggars belief" and that it is an insult to record stores that have supported Prince throughout his career.
Prince's label broke off ties in the UK with the album in an attempt to appease record stores.
The Mail on Sunday, like many newspapers, has given away free CDs before. A previous promotion included a free copy of Mike Oldfield's 1973 album 'Tubular Bells', a move which sparked a row with the musician over the likely effect on sales.
The paper maintains that its covermount CDs stimulate interest in music and that its 'Tubular Bells' giveaway lifted the album's sales in stores.
The Mail on Sunday also gave away a UB40 CD. The Sunday Express gave away a two-part Sandie Shaw CD, The Sunday Times gave away a punk CD and The Sunday Telegraph gave away a series of Horrible Histories CDs.
The Daily Mail reported an ABC for May of 2,294,929, down 0.24% month on month, down 3.99% year on year.