Microsoft Corp. is being investigated by U.S. authorities over potential bribery and corruption related to software sales in Hungary, according to people familiar with the matter.

The investigation follows a series of similar probes into Microsoft business partners that surfaced in 2013 in five other countries. Microsoft made a push earlier this decade to expand in emerging markets, as well as smaller, middle-income countries like Hungary. In some cases, those bets have turned into legal and reputational challenges.

The...