Franklin's office says the Queen of Soul broke ribs and has abdominal pain from Sunday's fall. Franklin says her doctors advised her to undergo tests.
She says efforts are under way to reschedule the canceled concerts for late August.
In a statement released Tuesday, Franklin says she was "very much looking forward to being in Brooklyn and having a foot-long hot dog at Coney Island."
The concerts were set for Monday and Aug. 12.
Franklin also was to perform at an Aug. 11 birthday party for U.S. Rep. Charles Rangel, D-N.Y.
On July 27, Franklin performed with ex-Secretary of State Condoleezza Rice at a children's programs fundraiser in Philadelphia.