no. 850 for the year 2005 which includes the following:

I am a mother of five, and due to my poor health, physicians advised me against having more children because a future pregnancy would be unsafe for me. They advised me to undergo tubal ligation. Is this permissible?

Prohibition of tubal ligation without a necessity
Permanent sterilization without a necessity is prohibited since it terminates procreation which undermines the need to protect human lineage i.e. one of the five necessities (life, intellect, religion, property and honor) which Islam has made among its objectives. 

Tubal ligation is permissible when there is a necessity 
If a future pregnancy would threaten the mother's life and trustworthy physicians determine that permanent sterilization is the only solution, it is permissible and the inquirer will not be blameworthy.

Allah Most High knows best.