Police Scotland said the rubbish had been piled up against a fence at the store between Old Shettleston Road and Cockenzie Street and was torched at 1.15pm on Wednesday.
The fire spread into the compound at the back of the store and caused an explosion in electrical units.
Detective Sergeant Colin MacRitchie said the fire caused a power blackout to nearby homes during the afternoon.
He said: "Not only was the setting of this fire irresponsible, it was also very dangerous and could have caused serious injury.
"Thankfully, on this occasion, no one was hurt, however, a number of homes in the area were without power for two hours as a result of this reckless act.
"The cost of the damage to Tesco runs into hundreds of thousands of pounds as there was substantial damage within the compound, to the electrical units and to stock."
He said police had established there were a number of children - pupils from a nearby school - in the area on their lunch break.
He added: "It is possible they may have seen someone setting the fire or acting suspiciously in the area so I would appeal them to contact police with information that may help us with our inquiries.
"The path between Old Shettleston Road and Cockenzie Street is used as a short cut by local people heading to and from Greenfields and is over looked by a number of residential properties. Again, I would ask that those who use the short cut or overlook the path contact police via the non emergency number 101."
Information can also be given anonymously to Crimestoppers on 0800 555 111.