The spinner, 28, will not play in the potential title decider at Middlesex after initially saying he needed rest.
Yorkshire are second in Division One and nine points adrift of Middlesex.
"I didn't feel that I am in a strong enough mental frame of mind to be at my best," said Rashid on social media.
"Although I did make myself available, if I was required to play I felt I could be letting the lads down.
"But coupled with my personal reasons I have also had a heavy period of cricket recently for Yorkshire and England which has been both physically and mentally draining and it is very unfortunate timing."
Yorkshire, who are looking to win their third-successive Championship title, will also be without Jonny Bairstow for this week's match at Lord's after the England & Wales Cricket Board (ECB) refused their request to field the wicketkeeper-batsman.
Rashid has been included in the squad for England's tour of Bangladesh in October.
"Family comes first for me and I will be away on England duty this winter with a busy playing schedule," he said.
"I have been in touch with the Yorkshire players and coaches and I will be wishing the lads all the best this game and I am desperately hoping we can lift the trophy for a third year in a row."
England all-rounder Adil Rashid says the illness of a "close family member" is why he asked to be left out of Yorkshire's final Championship match of the season on Tuesday.