Blair ordered the indefinite suspension on Jan. 1, according to a spokesman for Toronto Police Service.
The practice allows officers to stop people on the street and collect information such as their height, weight, hair and skin colour.
Toronto police have consistently defended the practice, arguing it is an "effective tool" in making communities safer. But carding has also drawn criticism.
Members of the public recently called on the police board to end the practice, citing numerous studies and even a board-sanctioned report that found carding policies generally tend to discriminate against visible minorities.
In the spring, carding policy was amended to limit when officers can card a citizen, and also required police to provide a receipt of the transaction to the person they have carded.
Blair is expected to provide an update on carding at the police board's meeting in February. Blair's term as chief will end in April.