Skov was born in San Francisco, California to Peter Skov, a white American, and Terri Skov, an African American.
His mother was diagnosed with multiple sclerosis and as a result the Skov family moved to Guadalajara, Jalisco for its mild climate and affordable healthcare. Shayne and his brother Patrick first began playing football in a team named Carneros de Guadalajara. He is a naturalized citizen of Mexico.
Skov attended the Trinity-Pawling School in Pawling, New York. He helped Trinity-Pawling to Erickson Conference and New England Prep titles as a senior, and was named 2008 Erickson Conference Player of the Year. He recorded 61 tackles (42 solo) as a senior. He also lettered in basketball and track and field. He participated in the 2009 U.S. Army All-American Bowl in San Antonio, Texas, where he recorded seven tackles including three for loss. Considered a four-star recruit by Rivals.com, he was rated as the 3rd best inside linebacker prospect in the nation. He committed to Stanford over offers from Duke, Boston College and Northwestern.
As a freshman in 2009, he appeared in all 13 games, making seven starts at outside linebacker. He finished third in the team in tackles with 62, including three for loss. As a sophomore, he went on to being named a conference honorable mention after recording 84 tackles (50 solo), including 10.5 for a loss, 7.5 sacks, two forced fumbles and five pass break ups. His season was highlighted by a 12 tackle, 3 sack performance against Virginia Tech in the 2011 Orange Bowl. In his junior season, he suffered a season-ending injury against Arizona in Week 3, but allowed him to be granted a medical redshirt. He finished the season with 19 tackles, including five for loss and one and a half sacks. In 2012, after missing the season opener against San Jose State for a DUI during the off-season, he started in 13 games, recording 81 tackles, including nine tackles for loss and 2.5 sacks and was named a conference honorable mention. In his final season, he went on to set a career high in tackles (109), tackles for loss (13), sacks (5.5) and forced fumbles (3). He was named a third team All-American by the Associated Press.
Skov signed with the San Francisco 49ers as an undrafted free agent. He was released during final roster cuts, but re-signed to their practice squad on August 30, 2014.