"Google's arbitrary and capricious treatment of Gabbard's campaign should raise concerns for policy makers everywhere about the company's ability to use its dominance to impact political discourse, in a way that interferes with the upcoming 2020 presidential election," the lawsuit said.
Google, however, said it had automated systems that flag unusual activity on advertiser accounts - including large spending changes - to prevent fraud, said Jose Castaneda, a spokesman for the company.
"In this case, our system triggered a suspension and the account was reinstated shortly thereafter. We are proud to offer ad products that help campaigns connect directly with voters, and we do so without bias toward any party or political ideology," he said.
Gabbard and her campaign are seeking an injunction against Google from further meddling in the election and damages of at least $50 million, the report said.
"Google's discriminatory actions against my campaign are reflective of how dangerous their complete dominance over internet search is, and how the increasing dominance of big tech companies over our public discourse threatens our core American values," said Gabbard, a co-Chair of the powerful House India Caucus.
"This is a threat to free speech, fair elections, and to our democracy, and I intend to fight back on behalf of all Americans," she said in a statement.
The lawsuit also said the Gabbard campaign believed its emails were being placed in spam folders on Gmail at "a disproportionately high rate" when compared with emails from other Democratic candidates.
Roughly half of the candidates who participated in the first Democratic debates have bought ads to appear at the top of search results for their names, the report said.
The Iraq war veteran has become the first-ever Hindu to be running for the presidency in the US
Gabbard, who converted to Hinduism early in her life and has become the first-ever Hindu to be running for the presidency in the US, is highly popular among Indian-Americans.
She supported Senator Bernie Sanders against former secretary of state Hillary Clinton in the 2016 Democratic primary.