Astle, who hit the fastest Test double century off just 153 balls against England in Christchurch in 2002, was ruled out of the series in Sri Lanka after undergoing surgery for a hernia and on a patella tendon tear in his left knee.
"Both operations appear to have been successful and Nathan is now recovering at home," NZC medical adviser Warren Frost said.
Frost added that NZC hoped Astle would be ready to return for the tour of India in October.
The first Test against Sri Lanka is in Colombo and starts on Friday. The second game in the two-Test series is in Kandy and starts on May 3.