The announcement came after Kronfeld had scored during Leicester's 27-17 Zurich Premiership win over Rotherham Titans at Millmoor on Saturday.
The victory was the Tigers' first Zurich Premiership away win since February.
Kronfeld has been captaining Leicester during the Rugby World Cup in Martin Johnson's absence, but will leave for New Zealand after next week's clash with Bath.
"I thought Josh was outstanding today, as he had been all season, but next week will be his last game for Leicester as he is returning to New Zealand," said Richards.
The Leicester coach has put off a decision on when his England internationals will return to domestic action after their World Cup Final win over Australia on Saturday.
His seven England stars will be back at the club on Wednesday, and Richards said: "There'll obviously be some mixed emotions, with a lot of guys coming back and it will depend on who might want a rest, so we shall see how they feel."