Fire crews attended the blaze after the alarm was raised at Ratheen Avenue shortly before 6.30am on Friday.
Three oil tanks were alight when crews arrived. They were destroyed in the incident.
A house and four occupied flats were also damaged, the Northern Ireland Fire and Rescue Service said.
"Firefighters wearing breathing apparatus used foam jets to combat the blaze," a spokesperson said.
Police said the cause of the fire is being treated as suspicious.
SDLP Chairman of Cookstown Borough Council Tony Quinn has condemned the arson attack.
This is very sinister and I'm thankful that nobody was injured in this attack.
Mr Quinn said a wheelie bin was set alight near one of the oil tanks, adding the properties could be uninhabitable for a number of weeks.
"Four or five homes have been affected and there is a sense of anger that so many lives were put in danger.
"I have been speaking to the Housing Executive and there are indications that the families affected could be out of their home for anything up to eight weeks. This is a disastrous way for families to start the New Year.
"I have been in contact with the local area district commander and I have no doubt that the PSNI will do all in its power to get to the bottom of this and find those responsible," he added.
A Housing Executive spokeswoman said: "We have not yet been able to access the properties as they remain cordoned off. As soon as we have access to the site the assessment of the damage is a priority.
"We are, at the present time, working with the families concerned to ensure they have accommodation to go to tonight and until they can return to their homes."
Police in Cookstown have appealed for information.