The 28-year-old Naved, who has played eight Tests and 45 One-day internationals, suffered the injury while playing for Sussex county during the ongoing local season and returned home last week.
Naved's injury was the latest blow to Pakistan's build-up for the tour after fast bowler Shoaib Akhtar was ruled out of the series last week due to an ankle injury.
Naved took 34 wickets in five matches for Sussex and was expected to spearhead Pakistan's attack in the four match Test and five match One-day series starting July 13.
"I have hopes of getting fit in time to face England. If not, it would be a great disappointment because I have been waiting for this series," Naved told AFP before his departure on Saturday.
"When I suffered the injury during a county match I felt pain even in walking but the injury has responded to treatment and now I can run with little discomfort," said Naved.
Pakistan captain Inzamam-ul-Haq blamed English county Sussex for Naved's injury.
"I think he was excessively used in (county) matches and not provided proper rest. Teams have to use fast bowlers very intelligently to avoid any burnouts or injuries," Inzamam said in an interview with a local newspaper.
Pakistan fly out on June 25 and play the first Test at Lord's.
Pakistan coach Bob Woolmer feared if Naved's injury was a Gilmore's Groin (named after the surgeon who discovered the injury), which involves tears to the adductor muscles, then the pacer would need surgery and could miss three months of cricket.
Meanwhile, Pakistan is considering including veteran leg-spinner Mushtaq Ahmed for the England tour and Akhtar if medical reports clear him.
Mushtaq has not played for Pakistan since 2003 but has been doing well for Sussex in the English season.