Arts House Limited (AHL), which presents the festival, and festival commissioner National Arts Council (NAC) announced the decision in a statement on Monday (May 18).
The extension will allow Mr Kripalani to finish his three-year arc as festival director, the statement added.
Mr Kripalani said in the statement: "It was heartbreaking for us to make the necessary decision not to go ahead. I would like to thank AHL and NAC for the chance to move as many of the shows as possible from this year to next year, especially the four Singapore commissions."
The commissions - Three Sisters by Nine Years Theatre, Oiwa by The Finger Players, The Year of No Return by The Necessary Stage and A Dream Under the Southern Bough: Existence by Toy Factory Productions - will now premiere at next year's festival.
Mr Kripalani told The Straits Times: "We are also talking to some of the international artists to see if they are available next year in order to be able to complete the three-year arc.
"In addition, I also want to programme new content that reflects the zeitgeist of our time."
Natalie Hennedige, who was due to take over the helm from Mr Kripalani, will now take over the festival from 2022 to 2024.
AHL's chief executive officer Sarah Martin said: "In this day and age, it is important to be able to adapt to changing situations, and Sifa continues to embody the spirit of adaptability and evolution."
The festival has been organising digital programmes in lieu of live performances, and will continue to do so this year.