Quanta Computer is a manufacturer of many flagship Apple products, including its MacBook line.
The hackers, known as Revil, have published stolen blueprints for unreleased products, and are threatening to release more.
Taiwanese officials said they are "taking an initial step to look into and understand" the incident.
It is being handled by the Ministry of Justice's investigation bureau.
On their darknet website, the anonymous hackers are attempting to extort a ransom from Apple directly, writing: "We recommended that Apple buy back available data by 1 May."