This comes as the Financial Action Task Force (FATF), an international body that sets standards on how countries combat money laundering, threatened Afghanistan with the punishment earlier this year.
The body had also warned that the failure by Afghan government to pass key measures means that it could be blacklisted in the month of June.
Afghan lawmakers in the lower house of the parliament (Wolesi Jirga) approved the law last Monday which was then passed to the Afghan senate house for approval.
The law will be passed to President Karzai after it was approved by Afghan senators.
Anti-money laundering law is part of a two-part legislative initiative designed to combat money laundering, corruption and the financing of terrorism.