Mixed race Noah Becker was referred to as a "little half-negro" in a tweet posted to the politician's Twitter handle but Mr Maier denied writing the tweet, which has since been deleted blaming one of his staff members for it.
The tweet was in response to an interview the 23 year old gave where he described Berlin as "a white city" compared to other European capitals, and said he had been attacked there because of his skin colour.
Mr Maier is the parliamentary deputy for the AfD party which received almost 13% of the vote and won over 90 seats in last year's election.
"I have been retained to quickly take the necessary steps under criminal and civil law against MP Jens Maier on the basis of this clearly racist tweet," Becker family lawyer Christian-Oliver Moser told a German newspaper.
Two other members of Mr Maier's far-right AfD party are under investigation over anti-Muslim messages they posted on New Year's Eve.
A new anti-hate law which came into force in Germany in the new year require social media companies to act quickly against hate speech or face a fines of up to 50m euro.