Islam encourages us to reproduce and have many children. A man came to the Messenger of Allaah and said: I have found a woman of good lineage, but she cannot have children. Should I marry her? He told him not to do that. He came to him a second time and he told him not to do that. Then he came to him a third time, and he told him not to do that and said: “Marry the one who is fertile and loving, for I will be proud of your numbers.” Narrated by Abu Dawood (2050), al-Nasaa’i (3227); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
This is one of the aims of marriage, which is to produce a Muslim child who will be given a righteous upbringing and who will benefit his family and his nation. This is one of the blessings whose value cannot be known except by the one who is deprived of it. Allaah has made children an adornment of life, as He says (interpretation of the meaning:
“Wealth and children are the adornment of the life of this world. But the good righteous deeds that last, are better with your Lord for rewards and better in respect of hope”
It is not permissible for a woman to prevent having children except in cases of real necessity, such as if pregnancy poses a danger to her life.
It says in a report of the Islamic Fiqh Council, issued during its fifth conference in 1409 AH/1988 CE:
Firstly: it is not permissible to promulgate a law which limits a couple’s freedom to have children.
Secondly: It is haraam to remove the ability to produce children for both the man and the woman, which is known as sterilization, except in cases of necessity as defined by sharee’ah.
Thirdly: it is permissible to stop reproduction temporarily so as to space out pregnancies, or stop them for a specific length of time, if there is a legitimate shar’i need to do so, if that is decided by both spouses with mutual consultation and agreement, so long as that will not result in any harm and so long as the means used are permissible according to Islam, and there is no transgression against an existing pregnancy. And Allaah knows best.
End quote from Majallat al-Majma’ (5/1/748).
Based on that, it is not permissible to have one’s tubes tied in order to prevent pregnancy permanently, except in cases of necessity. Now you have to have them untied if that will not result in harm.
See also question no. 20168.
And Allaah knows best.