In their draw at AZ Alkmaar, Fabregas, who missed Spain's clash with Bosnia-Herzegovina last week to be with his seriously ill grandfather, was making his second appearance for the Gunners in four days.
Clichy said: "In the dressing room and on the pitch, Cesc has been a good example for everyone.
"Sometimes you go through bad moments in your life and maybe this is one for him, but we are there for Cesc.
"He showed his character against AZ. I hope everything will be good for him and his family. On the pitch, he is still the big man."