Former Blue Bulls coach Meyer joined Tigers at the start of the current season and has presided over 11 wins and a draw in the opening four months of the season in the Guinness Premiership, Heineken Cup and EDF Energy Cup.
He has been joined at Leicester by his wife and family, but they are to return to South Africa due to serious family illness.
The Board of Leicester Tigers respects Heyneke’s position and the club offers him and his family its full support. The extent of his absence will be assessed over the next two weeks and kept under review.
During his absence, Heyneke will maintain communication with the coaching staff, who will be led by Richard Cockerill.
Leicester Tigers chief executive Peter Wheeler said: “Heyneke has made a big impression on everyone at the club since his arrival but we understand the situation he is in and we offer all of the support we can to him and his family.”