The Serbian hung in for the opening exchanges, but she soon became frustrated by Kvitova's power as the Czech took the first set 6-2.
It was much the same in the second as Kvitova found a break of serve at 2-2. However, with her opponent looking as if she was on the way to a comfortable victory, Ivanovic broke back at 4-5 before taking the set to a tie-break.
Despite her endeavour, Ivanovic was brushed aside in the tie-break as the world number two closed out the match 7-2.
The 21-year-old will face either Italy's Sara Errani or China's Jie Zheng in the last eight.