The man had slight injuries and needed first-aid treatment. All other bystanders, including the baby, got a lucky escape, Joinfo.com reports with reference to Mirror.
The explosion would have been caused by the contact between a spare lithium-ion battery and metal objects such as keys.
Fire investigator Jamie Lister said: “This footage clearly shows the dangers of storing batteries alongside any metal objects, be it keys, coins, or even your phone if it has a metal case.
It is not the first time that e-cigs explode and even cost lives. In 2014, a 62-year-old man from England was found dead in his home after an e-cig exploded and set fire to his oxygen concentrator.