The 27-year-old, learned the wife of his brother Tom -- a Leicester Tigers and England team mate -- was terminally ill with cancer having battled the illness for three years.
Youngs was included in a 41-man squad for his second tour but informed head coach Warren Gatland of his decision to withdraw this weekend.
"We are a very close family and, as I am sure everyone can respect, time is now precious together," Youngs said in a Leicester statement.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"The most important thing for me at this difficult time is to be able to offer as much support as I can to Tom and his family in the remaining time we all have together.
"It is a great honour to be selected as a member of the British & Irish Lions squad and I would like to thank Warren Gatland, the staff and the other players for their understanding in this situation.
"I wish them well and, like all rugby supporters in British and Ireland, hope they have a successful tour."
Both Ben and Tom played in Leicester's 28-23 victory against Worcester Warriors on Saturday and will feature in their Premiership semi-final against Wasps in two weeks.
The Lions tour begins on June 3.
(Reporting By Tom Hayward, editing by Pritha Sarkar)
