Gauland, 78, is one of the most prominent figures in the populist “Alternative for Germany” party, which rails against immigration, Islam and environmentalism.
On Thursday, German parliamentarians voted to remove his legal immunity to facilitate the probe, first reported by German media last March.
Frankfurt prosecutors said they would search Gauland's properties on Thursday as part of the investigation.
A spokesperson for AfD told AFP that the investigations concerned “old proceedings from the year before last”, adding that the party would give a further statement later Thursday.
The case is not believed to be related to recent investigations into other AfD politicians over illegal party funding.
Last April, the party was fined more than €400,000 ($450,000) for having received illegal campaign contributions during regional elections.
The blow prompted the party's treasurer to write to members last month that it is in “serious financial distress”.
Founded seven years ago, the AfD is now Germany's largest opposition party in terms of parliamentary seats.
In recent years, it has celebrated unprecedented electoral successes, entering the national parliament for the first time in 2017, but has also caused outrage with its challenge to Germany's culture of remembrance for Nazi crimes.
In 2018, Gauland said that the 12-year dictatorship of Adolf Hitler, which oversaw the systematic murder of six million Jews, was a “speck of bird shit in more than 1000 years of successful German history”.
AfD chairman for two years until he gave up the post last year, Gauland is still the party's parliamentary leader in the German Bundestag.