Under current law, an "infamous" crime, for the purposes of the Fifth Amendment, is one which carries a sentence of imprisonment for more than one year, or death. In other words, "infamous crime" is now a synonym for "felony".
For context, the Fifth Amendment reads:
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury [...]
So the definition of "infamous" would control which crimes must be prosecuted by an indictment from a grand jury.
The Federal Rules of Criminal Procedure, Rule 7 describes which crimes must be prosecuted by indictment, and its accompanying notes link this to the "infamous" criterion:
(a) (1) Felony. An offense (other than criminal contempt) must be prosecuted by an indictment if it is punishable: (A) by death; or (B) by imprisonment for more than one year.
Note to Subdivision (a). 1. This rule gives effect to the following provision of the Fifth Amendment to the Constitution of the United States: “No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury * * *”. An infamous crime has been defined as a crime punishable by death or by imprisonment in a penitentiary or at hard labor, Ex parte Wilson, 114 U.S. 417, 427; United States v. Moreland, 258 U.S. 433. Any sentence of imprisonment for a term of over one year may be served in a penitentiary, if so directed by the Attorney General, 18 U.S.C. 753f [now 4082, 4083] (Commitment of persons by any court of the United States and the juvenile court of the District of Columbia; place of confinement; transfers). Consequently any offense punishable by imprisonment for a term of over one year is an infamous crime.