The definition of supplier as found in ISO9000 is - the supplier of a product or a service (not verbatim) so the quick answer is yes.
The normally accepted "rule of thumb" is that the requirement applies to all suppliers of product or service used in production. This would not apply to office supplies, furniture and coffee used in the break room.
If the tooling is used in the production of your product or in any way effects the quality of the process or the satisfaction of the customer, the supplier is required to have at least ISO 9001:2000.
I hope this helps
Dave