Liebmann studied botany at the University of Copenhagen, although he never obtained a formal qualification.
He went on study tours of Germany and Norway before becoming lecturer at the Danish Royal Veterinary School in 1837.
In 1840 he travelled to Cuba and Mexico; on his return in 1845 he was appointed Professor of Botany at the University of Copenhagen.
He became Director of the university's Botanical Garden in 1852, a post he held until his death four years later.
Liebmann is commemorated in the scientific name of a species of Mexican snake, Chersodromus liebmanni.