Jacob Augustus Geissenhainer (August 28, 1839 – July 20, 1917) was an American lawyer and Democratic Party politician who represented New Jersey's 3rd congressional district in the United States House of Representatives for three terms from 1889 to 1895.

Geissenhainer was born in New York City and attended private schools.

He graduated from Columbia College in New York City (Master of Arts, 1858), and went on to study law at Yale Law School, and New York University (Bachelor of Arts, 1860).

In 1862 he was admitted to the bar, and he commenced practice in New York City.

Geissenhainer was an unsuccessful candidate for reelection in 1894 to the Fifty-fourth Congress.