Smith, who was suppose to play for Pune Warriors in the Indian Premier League, was ruled out before the tournament started as he required an operation on his left ankle, which had been troubling him for two months.
South Africa cricket team manager Dr Mohammed Moosajee said he was happy with Smith's progress.
"I am satisfied with (Smith's) progress thus far," Moosajee told the Afrikaans daily Beeld.
"His operation was a success and it is now all about rehabilitation," he added.
He underwent an operation and the plaster cast around his left ankle was removed earlier this week.
Moosajee said Smith should also be ready for the warm-up games, where the visitors will play against county sides Somerset over two days and Kent for three days before the first of three Tests starts at the Oval in London on July 19.
Although the second Test at Headingly will be Smith's 99th Test with South Africa, he also played one in Australia in 2005 for the World XI, thus this would make it a century of Tests for him.
The third and the final Test at Lords will also be a milestone for another South African veteran, wicketkeeper Mark Boucher, as it will be his 150th match.
Boucher is expected to retire after the England tour. PTI FH CM
