The nominations, along with those for other cabinet posts, were made on Thursday at the start of a consultation process with Greens members to ratify the coalition deal the party has agreed with the Social Democrats, or SPD, and Free Democrats, or FDP.
Baerbock would be Germany's first female foreign minister.
The Greens nominated Cem Ozdemir, a former party leader, as agriculture minister. The son of a textile factory worker and a teacher who came as guest workers in the 1960s, he will be the first member of Germany's three-million-strong ethnic Turkish population to serve as a federal minister.
The three coalition partners unveiled their vision on Wednesday of how to push through a green transition in Europe's biggest economy, speed up digitalisation and bring in some liberal social policies.
The Greens also put forward senior party figures Anne Spiegel as family minister and Steffi Lemke as environment minister.
The three parties have written into their coalition deal how they will divide up the cabinet posts.
The results of the 10-day vote of 125,000 Greens members on the coalition agreement are expected during the first weekend in December, around the same time as the SPD and FDP expect to ratify the deal. This would mean the SPD's Olaf Scholz could succeed Angela Merkel and become chancellor in the week of Dec 6.