I believe, but cannot say definitively, that the very first audience ratings for television — covering the New York City area — were released on March 4th, 1948 by C.E. Hooper, Inc. It was certainly the first report issued by Hooper and as far as I know it was the first to venture into the field of television ratings. In The Magic Window: American Television, 1939-1953, James Von Schilling calls this report “the TV industry’s first official ratings” . Earlier attempts to evaluate television’s audience were made, unofficially, by mailing cards to television set owners.
Topping this first Hooper report was DuMont’s The Original Amateur Hour, or at least its broadcast in New York City over WABD from 7-8PM on Sundays. It drew a 46.8 rating according to an article in The New York Times by Jack Gould . Unfortunately, Gould doesn’t give the time frame covered by the report, noting only that the report was “the first popularity poll of television programs” . Thus, there’s no way of knowing whether the report covered a single week or a whole month.
Furthermore, Gould doesn’t include additional ratings past The Original Amateur Hour, writing that “the survey organization [explains] that more complete reports would be forthcoming at a later date” . He does point out that the 46.8 rating for WABD’s broadcast of The Original Amateur Hour was the highest Hooper rating since 1936 when the radio version of The Original Amateur Hour, hosted by Major Edward Bowes, had a 46.9 .
(The Original Amateur Hour began on radio in 1934 and was hosted by its creator, Major Edward Bowes, until 1946. Ted Mack then took over as host. A television version premiered on Sunday, January 18th, 1948 on DuMont, also hosted by Mack. The radio version ended in 1952; the television version would run on all four networks before finally ending in 1970.)
An earlier article in The New York Times, published on January 13th, 1948 and also written by Jack Gould, reported on Hooper’s entry into television ratings:
For the present his video poll will be confined to the New York area, the research specialist having obtained a list of 10,000 television set owners from various industry sources. In the main the survey will be similar to Mr. Hooper’s examination of the radio field, except that television set owner’s will have an opportunity to report whether they think a program’s quality is “good,” “fair” or “poor.” The radio poll does not make provisions for any statements [about] a program’s quality. 
I’m assuming that “the New York area” mentioned in the article is New York City, as later Hooper reports make clear. One such article in The New York Times, this one published on April 29th, 1948, included the following paragraph:
The Circus, in chalking up a mark of 67.2 in television, was described as “the highest-rated program in the April New York City Teleratings issued yesterday by C.E. Hooper, Inc.” 
I’m afraid I’m not sure what “The Circus” is. There were four broadcasts of the actual circus — that of the Ringling Brothers and Barnum & Bailey — from Madison Square Garden during the month of April, all on CBS and its WCBS-TV station in New York City. One of these broadcasts could be the program mentioned in the article. Only two were shown at night, however, those on Wednesday, April 7th and Wednesday, April 21st. The others were matinees on Sunday, April 11th and Sunday, April 18th .
Hopefully the actual Hooper reports from these early months exist somewhere, with detailed information on the time frames involved and full listings of programs rated. I wouldn’t even know where to look, though. Perhaps the Library of Congress?
2 Gould, Jack. “Radio News.” New York Times. 5 Mar. 1948: 40.
5 Gould, Jack. “News of Radio.” New York Times. 13 Jan. 1948: 50.
6 “Radio News.” New York Times. 29 Apr. 1948: 44.
7 “Radio News.” New York Times. 5 Apr. 1948: 42.