In his 40s, Khan was representing Old Concordians Cricket Club in a match against Prince Alfred Old Collegians last Saturday, news.com.au reported.
After fielding for 40 overs and batting for seven, Khan collapsed around 4pm Australian Central Daylight Time (ACDT).
South Australia has been in the grip of extreme heat over and according to data from the Bureau of Meteorology, temperatures here were still above 40 degrees Celsius at the time.
Adelaide Turf Cricket Association rules state that games are cancelled if the temperature climbs above 42 degrees Celsius.
"We are deeply saddened by the passing of a valued member of the Old Concordians Cricket Club, who tragically suffered a medical episode while playing on the Concordia College oval today," Khan's club said in a statement.
"Despite the best efforts of paramedics, he sadly did not survive. Our thoughts and heartfelt condolences are with his family, friends, and teammates during this difficult time."
Khan had reportedly moved to Adelaide from Pakistan in 2013 to work in the IT industry.