He went to a roti shop in Toronto's Parkdale neighbourhood at about 7:45 p.m. on Saturday.
Logan ordered his food and was waiting outside with his dog while the food was being prepared.
"A man approached me…he asked if the roti shop was still open, I said yes," Logan told CBC News on Sunday. "He was in there for about a minute and as he left the store, I entered to pick up my food and then one of the staff members saw him bend down and pick up the dog, assuming he was the owner."
Logan's dog's name is Poochie and he's a 14-month-old miniature poodle.
He said only let Poochie out of his sight for 10 to 15 seconds, so that he could pay for the food.
Logan initially assumed that his dog had broken his collar, but upon realizing that nothing was attached to his leash, he "assumed the worst."
No one saw the man with Poochie on Queen Street West, or Dunn Avenue. As a result, Logan believes it is likely the man who took his home went into a nearby building.
Logan reported the theft to police, but he is "very worried" about his dog.
"He's got a home, he's very loved, he's a very important part of our family and just it tears you inside out not knowing where he is, if he's safe, if he’s being mistreated, if he's being treated well, if the plan is for him to be sold or if the plan is for him to be kept," said Logan.
"But, you know, he already has a very loving home and a loving family and we just want him to be returned."
Police are investigating the matter and Logan has put posters up, advising the public about the theft of his dog.