The answer is not many. It was 1939, television was brand new and almost no one had a set. Nonetheless, they tried a near-experimental broadcast over the rarely seen medium as part of the New York World's Fair. It's estimated only 3,000 people saw it. 

Not that they were exactly watching a classic. 

"If you were one of the lucky few to watch Major League Baseball on television, you didn't exactly see a classic either. The Dodgers scored two runs in the bottom of the second inning thanks to a passed ball and throwing error, then not much happened until the Reds pushed five runs across in the eighth in an inning that included two errors, a bases-loaded walk and the ever-thrilling sacrifice fly. The real excitement, though, was the technology behind the broadcast rather than the game itself."

When you consider that every single game is now available to viewers on a daily basis, it's amazing to consider what those few viewers would have thought of how far things have come.

87 Years Ago, TV Aired Its First Major League Baseball Game—to About 3,000 People