Atapattu, 35, who was picked in the 16-man squad subject to a fitness test, was ruled out by Sri Lankas medical staff for the three-Test series, chairman of cricket selectors Lalith Kaluperuma told AFP on Monday.
"When he sat out of the Pakistan series we were expecting that he would recover in time and be available for the tougher challenge in England, but he has failed to recover," said Kaluperuma.
"Obviously its a severe blow for us. He was our best batsman in England four years ago in the Test series and with him out we will find it extremely difficult to fill that slot."
Jehan Mubarak will replace Atapattu, but Sri Lanka will have an inexperienced pair at the top of the order with veteran opener Sanath Jayasuriya too having retired from Test cricket.
Mahela Jayawardene will lead the side in Atapattu's absence and wicket-keeper Kumar Sangakkara will be elevated as vice-captain.
Team physiotherapist Tommy Simsek said Atapattu may have to undergo surgery if he wanted to prolong his career.
"Marvans problem was that the disc bone on his back was touching a nerve and we were hoping that it would heal naturally with rest, but a scan a few days back revealed that theres no improvement," Simsek said.
"The only option available is that he has got to have surgery now."
Sri Lanka begins the tour with a three-day game against British Universities at Cambridge from April 24.
The first Test starts at Lord's on May 11, followed by the second Test in Birmingham from May 25 and the third in Nottingham from June 2.
Sri Lanka will also play a Twenty20 international at Southampton on June 15 before a series of five one-day internationals against England from June 17 to July 1.