[Siegmund]

No, he didn't.

The Nobel Prize in Economics was first awarded in 1969 and von Neumann died in 1957. There is no Nobel Prize in mathematics. The most prestigious mathematics award, the Fields Medal, is awarded only to mathematicians under age 40 and was not awarded regularly until 1950 when von Neumann was already too old to be eligible.

Had he lived longer it's interesting to speculate whether he would have gotten a Nobel, perhaps in physics but more likely in economics - but living to a ripe old age is a prerequisite for Nobels, it seems... John Nash published the Nash Equilibrium in 1950 but got his economics prize in 1994!

There is, incidentally, a von Neumann prize, too - awarded annually for theoretical contributions to operations research (a branch of applied mathematics) since 1975 - which was won by Nash, Blackwell, Shapley, and Arrow in its early years.