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Danish lawyer, botanist and politician. From 1821, professor in botany at the University of Copenhagen.

His main scientific field was the new discipline of phytogeography. He also served as director of Copenhagen Botanical Garden in 1841-1852. He was a leading figure in the National Liberal movement and president of the Danish Constituent Assembly in 1848.

He was already a lawyer when he in the summer of 1812 travelled to Norway with the Norwegian botanist Christen Smith. On this journey, he was impressed with the conspicuous zonal division of the mountain vegetation and distribution of plant species in relation to altitude. Back in Copenhagen, he attended the lectures given by Martin Vahl and J.W. Hornemann. While working a lawyer, he delved into the copious literature on plant geography, e.g. by Wahlenberg and von Humboldt. The first result of his efforts was a doctoral dissertation (1816): Dissertatio de sedibus plantarum originariis. In this thesis, he dealt with the question of Generatio aequivoca, that is the origin of species through continuous evolution, a view he advocated.

He was then given a travel grant to study phytogeography in Southern Europe and to visit A. P. de Candolle in Geneva. The expectations of his scientific potential were so great that King Frederik VI granted him an extraordinary professorship of botany at the University of Copenhagen. In 1822, his most significant contribution was published:

Grundtræk til en almindelig Plantegeographie. Copenhagen, Gyldendalske Boghandels Forlag.

A German translation was published the following year in Berlin: Grundzüge einer allgemeinen Pflanzengeographie, Berlin 1823.

He planned a great work and gathered material for it during two journeys to Italy. However, he never had time to continue his work. Together with Jens Vahl and Salomon Drejer, Schouw served as the publisher of Flora Danica fasc. 38.

He succeeded Jens Wilken Hornemann as director of Copenhagen Botanical Garden in 1841-1852. In 1841, he was elected a foreign member of the Royal Swedish Academy of Sciences.

In the 1830s and 1840s, Schouw was one of the main leaders of the political movement that led to the first democratic constitution of Denmark, the June Constitution of 1849. The king appointed him as a representative for the university for the first Roskilde Provincial Assembly in 1834 (a, a recognition of the growing importance of the liberal movement (but he belonged to the moderate wing), where he was immediately elected as its president with 37 votes against 18 votes to Lauritz Nicolai Hvidt and 11 votes to the Conservative bishop J. P. Münster. He was later reelected at Viborg Provincial Assembly with all votes against one and was reelected until 1840 when he was no longerappointed by the king, probably as a result of the government's discontent with his claim of the Provincial Assembly's independence. He was much engaged in Scandinavism and in the Schleswig-Holstein Question. He was a member of the 1848 Danish Constituent Assembly but refused to become a minister because he, unlike the government, favoured the division of Schleswig.

He published Dansk Ugeskrift in 1831–36 and again 1842–46, followed by Dansk Tidsskrift 1847–50.