"Younis has suffered a (family) tragedy and will miss the third match. At this moment in time we don't know whether he will be able to play the remainder of the series or not," Bari said on Friday.
Younis' brother Farman Khan died in Germany after a failed liver transplant.
This is the third personal loss Younis has suffered in the past two years. His father died in January 2005, and he lost a brother in November 2005.
Mohammad Yousuf, who missed the second match at Faisalabad to be with his wife who is expecting a child, will return to the 14-man squad for the third match to be played here on Sunday.
"Yuosuf will be available" because the match is being played in his hometown Lahore, Bari said.
Pakistan lead the five-match series 1-0 after a narrow two-wicket win in the second match on Thursday.
The first match was washed out due to rain in Rawalpindi on Tuesday.
The fourth match will be played at Multan on Dec 13, and the fifth match in Karachi on Dec 16.
Inzamam-ul-Haq (capt), Mohammad Hafeez, Imran Farhat, Yasir Hameed, Shoaib Malik, Mohammad Yousuf, Kamran Akmal, Abdul Razzaq, Rao Iftikhar, Umar Gul, Mohammad Sami, Rana Naved-ul-Hasan, Danish Kaneria and Abdul Rehman.