She was arrested last month on the suspicion of illegally importing the painkiller oxycodone in the mail.
The American became the firm’s chief communications officer and first female managing officer in April.
The world’s biggest carmaker said it had accepted Ms Hamp’s resignation after considering the concerns of its stakeholders.
It added that the investigation on the former executive was still continuing and there was “little” the company could say at the time.
“However, we intend to learn from this incident to help ensure a secure working environment for everyone at Toyota around the world as we continue to take the steps necessary to become a truly global company,” it said.
“We remain firmly committed to putting the right people in the right places, regardless of nationality, gender, age and other factors.”
Ms Hamp, 55, was a key female figure in the carmaker’s push for diversity at the company and her arrest made headlines in the local media.
Ms Hamp, meanwhile, is accused of importing 57 tablets of the prescription drug in a package labelled “necklaces” addressed to herself.
Oxycodone is a legal substance in the both the US and Japan, but can only be brought into Japan if it is carried by a person with a legitimate prescription.