The 22-year-old Nevin made 42 appearances for Ulster, including a Heineken Cup fixture against Tigers at Welford Road last season, and was named Young Player of the Year at the IRFU Players Association Awards.
Shane Logan, chief executive of Ulster Rugby, said: "Nevin was a wonderful player but also a wonderful person. He was well liked and his loss will be deeply felt by his team-mates and everyone at Ulster Rugby.
"He will be sorely missed and the thoughts of everyone involved in the game are with his family at this time."
On behalf of club officials, players and supporters, Leicester Tigers pass on condolences to all at Ulster Rugby and to family and friends of Nevin Spence.
Supporters are requested to make their way to their places in good time ahead of kick-off at 5.30pm on Saturday to allow the whole stadium to observe the minute’s silence.