The suspect, identified as 46-year-ld Elie Granger was charged with 2nd degree murder, assault in the first degree, and assault in the second degree.
He was described as a transient who likely lives in a shelter or on the street.
Detectives say they caught Granger after reviewing video from an NYPD surveillance camera near the area.
In Sunday's attack, 37-year-old Eduarda Oliva was stabbed in the chest at Queens Plaza North and 22nd Street.
She was attacked while walking with her 13-year-old daughter near the Queensboro Bridge.
She remains hospitalized at New York Presbyterian-Cornell Medical Center in stable condition.
Detectives believe Oliva was randomly targeted by the homeless man.