Wilcox, one of the Cowboys’ two third-round picks in the 2013 draft, left training camp Sunday to be with his family and has been excused all week.
"It’s tough for anybody," coach Jason Garrett said. "A young person, an adult, obviously a very difficult time. We have complete respect for what's going on in his life right now and want to give him all the opportunity to make sure he takes care of that the way he wants to. All the support systems are available to him. I think it's just a very difficult thing in life."
Wilcox had an interception and a team-high six tackles -- all in one drive -- in last week's preseason game against Oakland but will not play Saturday for the Cowboys in Arizona.
Despite playing safety for only one season at Georgia Southern, Wilcox has brought a physical presence to the secondary and has been among the team's most impressive young players.
After the draft, Wilcox spoke about how much it meant to him that his mother got to see him selected by the Cowboys.
ESPNDallas.com's Todd Archer contributed to this report.