A further 33 people at the Kuehne and Nagel depot in Draycott-in-the-Clay, Staffordshire, were seen by paramedics.
Two men and two women were taken to hospital in Burton-upon-Trent, and a man and a woman taken to Royal Derby Hospital.
The firm said "they are not in immediate danger".
More on this and other stories from Stoke and Staffordshire
West Midlands Ambulance Service said it was called to the site in Ashbourne shortly before 13:00 GMT on Monday after a woman reported feeling ill and it "quickly became apparent" she was suffering from the effects of carbon monoxide poisoning.
Ambulance officials said: "A number of other patients then began coming forward. Ambulance staff worked quickly to assess them all in order to establish the severity of their conditions."
A spokeswoman for Kuehne and Nagel said a "thorough investigation" is under way.
She added: "A number of people were given oxygen at the site and six were taken to hospital as a precautionary measure."
A logistics company has confirmed it is investigating after six members of staff were taken to hospital with suspected carbon monoxide poisoning.