Arenado, 22, was ranked as the 52nd best prospect in baseball before this season by Baseball America. He's hitting .364/.392/.667 with three homers, 21 RBI and 11 doubles in 18 games for Triple-A Colorado Springs and is also known as an excellent defender.
Nelson, 27, was the ninth overall pick in the 2004 draft. He hit .301/.352/.458 with nine homers and 53 RBI last season in 377 plate appearances, but struggled thus far in 2013. Through 21 games, he's hitting .242/.282/.318 with a double and two triples. He has also made three errors in 48 chances.
The Rockies started this season 13-4 but have since lost five of their past seven.
News of the move was first reported by Troy Renck of the Denver Post.