This isn't precisely a postcard, but it's the same size and dimensions. It's Post Cereals' Mighty Mouse Mystery Color Picture No. 1 from 1957. It was probably originally packed inside a box of Post Sugar Crisp1, as Topher's Breakfast Cereal Character Guide states that "Mighty Mouse championed Sugar Crisp in 1957."2
"Here the champion of the Mouse Kingdom, Mighty Mouse, is on his way to crush an evil plan. This mean character will try anything to win. What evil is behind is behind the walls of the house?The water was applied to front of the card long ago, as you can see above, revealing the villain to be "Sylvester the Fox in his laboratory."
"To find the answer just apply water to the picture with a brush or piece of cotton and -- presto! the answer appears in color. Collect all six Mighty Mouse color pictures and solve the other mysteries."
Some of the other card fronts from this series can be seen on the Neato Coolville blog.
1. Post Sugar Crisp is also mentioned in the July 10 Papergreat post "Breakfast ideas from Tang with a space shuttle theme."
2. Some other cartoon characters that "championed" Sugar Crisp, according to Topher's Breakfast Cereal Character Guide, were: Dandy, Handy, and Candy (three identical bears); Sugar Bear; Granny Goodwitch (voiced by Ruth Buzzi); and Li'l Abner.