Ivanovic told a news conference that she will miss next week's Sydney International but hopes to be fit for the Australian Open, which begins Jan. 17.
Isner lost to Andy Murray 6-4, 6-2 in the second singles match on Friday as the fourth-ranked Briton produced his most assured performance of the week.
The U.S won the match 2-1 when Britain forfeited the mixed doubles.
Mattek-Sands' power and consistency proved too much for the 16-year-old Robson, who received treatment for tightness in her right thigh on a day dominated by injuries.
That left the U.S. needing to win only once in its matchup against already-eliminated Britain, and Mattek-Sands delivered with her third singles win of the week.
After both the day's scheduled doubles matches were canceled, the U.S. took on France in an exhibition set. Mahut took to the court in a white dress, pink hairband, and knee-length socks, to the delight of the 7,508 spectators.