Berg was named to the first team while Kaprielian earned third team honors.
The Collegiate Women Sports Awards Show airs live Monday, June 29 at 6pm PT on CBS Sports Network.
UCLA coaching staff will also participate in the games
The Bruin men and women also post Top 10 finishes in the Capital One Cup.
UCLA's Kevon Looney and Norman Powell were each chosen in Thursday evening's NBA Draft.