Chelsea defender Terry was stripped of the England captaincy earlier this month following media allegations he had an extra-marital affair with Manchester City left back Bridge's former girlfriend.
Asked by reporters on Tuesday whether Bridge would be quitting international football, Capello replied: "No, he will be with us (next Wednesday). No problems about the other things".
Deputy left-back Bridge could feature in the starting line-up in the absence of first-choice Ashley Cole, who is expected to be out for the rest of the season with a broken ankle.
Capello said he would discuss Terry's removal as captain with the rest of the squad ahead of the game at Wembley.
"The World Cup (in South Africa in June) is really important for me, for England and the players," said the Italian at a pre-tournament workshop for coaches.
"We have to stay together and be compact in every moment. I think this will be my most important job, to recreate this spirit.
"After (a gap of) four months we will meet the players (again) next week and it will be a very important game for many reasons. One is also this (situation)," added Capello in a reference to Terry's removal as captain.
"We will talk about a lot of things because four months is a long time. If you can meet the players every month it is different."
Capello, who has a reputation as a strict disciplinarian, issued a veiled warning about possible future controversies.
"The players have to understand what I want if you want to stay with me," he said. "It will be very important because we need to create a group."
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