“We are due for our second baby and my wife's had a bit of a tough time, so I'm having to make sure she's alright. It's a bit open-ended as to when I'll be available for Yorkshire, but hopefully I'll be available for the start of the 50-over competition,” Willey said.
He also said CSK were very understanding and supportive, adding it was not an easy decision for him to take.
“Chennai were very understanding and very supportive, as have been Yorkshire. It's never an easy decision. But, nonetheless, it's the right decision. I need to put my family first and cricket's secondary to that. We'll get that sorted and then I can concentrate on cricket,” the 29-year-old said.
Last year, Willey was called up as a late replacement for an injured Kedar Jadhav by CSK and had been retained by the defending champions.
Meanwhile, CSK officials said they had not been informed by Willey about the decision to withdraw from this year's IPL.
The three-time IPL champion had suffered a blow ahead of the tournament when South Africa paceman Lungi Ngidi pulled out due to an injury. CSK has not yet named a replacement for him.