The gemara says that someone who goes to visit a sick person should say this (שבת היא מלזעוק ורפואה קרובה לבא) to the sick person. Rashi explains, we are telling the sick person to try not to be sad because it is shabbos and a person is supposed to be happy on shabbos. The Ran has a different peshat. He says we are telling the sick person that since it is shabbos we can't daven for him.
Rashi's peshat fits in better with the מי שבירך לחולים, we say the מי שבירך and then we tell the people in shul, don't be upset about the sick person it is shabbos. However, according to the Ran it is a bit difficult, we are contradicting ourselves, we just said a prayer for the sick person and we end off by saying we really aren't allowed to daven for you. Maybe the pshat is that we are explaining why this is the only tefilla we are saying for the sick person.