The project, which will make way for the new Dunedin Hospital, will be carried out in stages, bringing down one of three blocks at a time.
Thursday marked the first day of demolition work following a temporary pause due to Covid-19 restrictions.
Ministry of Health project director Mike Barns said starting with the warehouse was a good way to introduce the city to the demolition.
Bringing down the warehouse’s steel beams would be more manageable than the concrete structures of the two factory blocks.
A "soft strip" had begun throughout the factory, which meant removing the non-structural elements of buildings, including the internal walls.
While the project had fallen two weeks behind schedule due to the lockdown, it was expected the team would catch up on lost time quickly.
The warehouse would be completely removed over the next four weeks.
The full demolition would need to be completed by January 2022, a date which meant they had "time up their sleeves".
