Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, the late Saudi scholar, Sheikh Ibn Baz (may Allah have mercy on him) stated:
One must wash the clothing by splashing water over it if the child is breast feeding and does not eat hard food. It is similar to his urine, which is moistened with water and then one can pray in that clothing. The clothes are not to be prayed in until they are splashed with water.
Almighty Allah knows best.
Source: Islamic Fatawa Regarding Women, Compiled by Muhammad Ibn Abdul-Aziz Al-Musnad and translated by Jamal Al-Din Zarabozo, Darussalam, 1996.