The OFT wants to find out if the games put undue pressure on children to pay for additional content.
Many games ask players to pay to get coins, gems or other virtual items to speed their progress through levels.
The OFT wants to hear from parents who have seen firms aggressively pushing in-game content to children.
High cost The investigation comes alongside media reports about children spending large sums on virtual items for smartphone and web games.
In March, five-year-old schoolboy Danny Kitchen, from Bristol, managed to rack up charges of more than £1,700 while playing the Zombies versus Ninjas game on his parents' iPad. The money has since been refunded by Apple.
In its investigation, the OFT wants to find out if the games are "misleading, commercially aggressive or otherwise unfair" when they give people the chance to buy extras. It also wants to find out if children are being specifically targeted by such applications.
"We are concerned that children and their parents could be subject to unfair pressure to purchase when they are playing games they thought were free, but which can actually run up substantial costs," said Cavendish Elithorn, the OFT's senior director for goods and consumer.
Mr Elithorn said the OFT did not want to ban in-game purchases, but wanted to be sure that games-makers are complying with relevant laws. Consumer groups or parents with evidence of games aggressively marketing in-game extras should contact the OFT, it said.
Figures gathered by the OFT reveal that the vast majority of the most popular smartphone games were free to install but raised cash for their creators via in-app purchases. Such extras were priced very differently, it said, with some costing only a few pence but the most high-priced were £70.