On Tuesday a spokesman for the Berlin Prosecutor's Office confirmed that investigators searched Hebold's apartment and found evidence pertaining to the investigation.
"The investigation into incitement to hatred is ongoing," Martin Steltner told Berliner Zeitung.
Hebold, a university lecturer in statistics, was a controversial choice to become the party's candidate for the Lichtenberg district of Berlin. Earlier this year he was fired from three teaching jobs, including the University of Berlin, after allegedly making xenophobic comments during his teaching and on his blog called "The Devastation of Europe – a Diary of Decline."
According to Berliner Zeitung, Professor Hebold allegedly asked students on his course to carry out a number of mathematical tasks which had a political element. These included the calculation of the statistical relationship between the proportion of Muslims in the population of a country, and the number of terrorist attacks there.
However, in an interview with the newspaper Hebold denied that he was discriminating against Muslims.
"I am anti-Islamic, just as I am anti-Communist and anti-Fascist," Hebold said.
'House search: Wolfgang Hebold is being investigated for incitement to hatred," Berline Zeitung reported.
As a result of Hebold's alleged transgressions, Berlin representatives of Die Linke, the Social Democratic Party of Germany (SDP) and the Christian Democratic Union (CDU) have all announced their opposition to his candidacy. They also want to prevent Hebold from serving in an important electoral office, such as the Department for School and Youth.
However, earlier this month the Berlin AfD remained defiant amid the furor, which it called "undemocratic."
"Mr Hebold wants the swift clarification of this matter," said local AfD leader Dietmar Drewes.
Drewes criticized the press for publishing "pre-judgment scenarios" about Hebold, and also criticized the other political parties for their "extremely undemocratic" reaction to Hebold's candidacy.
"He is being defamed by the press. I would even go so far as to say that this approach is trying to destroy his existence," Drewes said.
The Eurosceptic, anti-immigration AfD was founded in February 2013 in response to the EU's handling of its debt crisis. The party rejects Turkish membership of the EU, wants a referendum on Germany's membership of the single currency, and proposes to repeal Germany's Renewable Energies Act.
In addition to Berlin, the party also made significant gains in elections in three other German states earlier this year. In Baden-Wurttemburg, Rheinland-Pfalz and Sachsen-Anhalt, the party received 15.1, 12.6 and 24.3 percent of the vote respectively, an indication of rising levels of support ahead of federal elections in autumn next year.