No. Male companions have been there from the very start of the show—in the first episode, the First Doctor and Susan picked up not just Barbara Wright but also Ian Chesterton. Besides Ian, some of the most famous male companions include Jamie McCrimmon (with the Second Doctor), K9 (Fourth Doctor), Adric (Fourth and Fifth Doctors), Jack Harkness (Ninth), and Rory Williams (Eleventh).
There was a period at the end of the classic series where the Doctor traveled with only one companion at a time, always female—Peri, then Mel, then Ace. And there was another period at the start of the new series where there was always a clear "main companion", always female—Rose, then Martha, then Donna (and maybe Astrid for one story in between). But neither is true for the show in general, it just happened to be true for a few years.
In fact, as of the end of series 9 (2016), the Doctor is currently traveling with only a male companion, Nardole. And that's not the first time—Steven Taylor, Vislor Turlough, and Wilfred Mott have all been sole companions, at least briefly.