She was taken in to custody on suspicion of sexually activity with the child - aged under 16 - during an alleged "inappropriate" relationship.
Goddard (pictured right) has been suspended from teaching while police investigate.
A spokesman for the City of London Corporation, which owns the school, said: "A member of staff has been arrested following an investigation by police in to an allegation of an inappropriate relationship with one of our students."
Worried parents of the 700 pupils at the school were asked to read a letter posted on the school's intranet by headmistress Diana Vernon.
The letter read: "The school takes its responsibility for the safeguarding of our children extremely seriously.
"We were pro-active in reporting this allegation and have since been co-operating fully with the police and authorities.
"As always, the wellbeing of our students is our paramount concern."
Miss Vernon added that Goddard had been suspended as a "precautionary" measure.
The school, whose former pupils include pop star Dido and TV presenter Claudia Winkleman, is based within the Barbican complex in the City's Square Mile. Its pupils are aged between seven and 18
A City of London Police spokeswoman said: "A 26-year-old woman from South London was arrested on July 20 on suspicion of sexual activity with a child.
"She has since been bailed and inquiries continue."