McMillan, has played 55 Tests and 191 one-day internationals and, following a recall to the New Zealand side in January, played in April's World Cup semi-final defeat against Sri Lanka in Jamaica.
The 30-year-old is currently playing for English north-west club side Nelson in the Lancashire League.
MCC secretary and chief executive, Keith Bradshaw, said: "I'm delighted that Craig has accepted our invitation to captain MCC against Sri Lanka 'A' next month. His talent and international experience will surely be a great asset to the team.
"Arundel is a wonderful setting in which to play and watch cricket. We hope that a substantial crowd will watch Craig lead MCC's team," added Bradshaw of a match that will be played in the grounds of Arundel Castle.
In his one-day international career, McMillan has scored over 4,500 runs and taken 46 wickets. The hard-hitting batsman also holds the record for the fastest one-day century scored by a New Zealand international - 117 off 67 balls against Australia earlier this year.
The game against MCC is the first fixture for Sri Lanka 'A' on their tour of England. Further details regarding MCC's full line-up for this match will be announced in due course, the club said.
It is nearly 40 years since MCC, which owns London's Lord's Cricket Ground, stopped running English cricket. However, globally, it remains responsible for the sport's laws.