The 26-year-old has torn his medial knee ligament and was replaced by Yuri Zhirkov during the game at Ewood Park.
The injury to the Serb will be a blow to Carlo Ancelotti’s Premier League title contenders, who are four points behind leaders Manchester United.
Ivanovic will now miss the crucial game against United on 3 April.
Chelsea have one game in hand on the Premier League champions, which comes against Portsmouth on Wednesday evening.
But Ivanovic’s injury adds further worry to a defence that is already without long-term absentee Jose Bosingwa and Ashley Cole, who is battling to be fit before the end of the season.
The Blues have only eight Premier League games left and Ivanovic is now likely to miss five of them in addition to the FA Cup semi-final against Aston Villa on 10 April.
Ancelotti will be desperate to win some silverware in his first season at Stamford Bridge after crashing out of the Champions League to Inter Milan last week.
Yet with only Paulo Ferreira, Juliano Belletti and Zhirkov left as recognised full-backs, Chelsea’s defensive cover is now looking thin.
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