Andreescu defied the odds to become the first wildcard to be crowned Indian Wells champion earlier this month, but there will be no Sunshine Double after the 18 year-old Canadian shook hands at 6-1 2-0 down.
A right shoulder injury halted the rising star's incredible run and ensured Kontaveit will face either Caroline Wozniacki or Hsieh Su-wei in the quarter-finals.
Kontaveit took charge after a rain delay of around 90 minutes and Andreescu called for a medical timeout after losing the first set.
It was all over just 56 minutes into the contest on Court 1, with Andreescu deciding she was unable to continue.
Andreescu had beaten Kerber - her opponent in the final at Indian Wells - to reach the last 16 after saving a match point in her defeat of Irina-Camelia Begu in the first round and got past Sofia Kenin in round two.
The teenager will go no further though, as the world number 24's exploits in the United States appeared to catch up with her.