Answer: pretty high (at least $12), but see below for qualifications and doubts. The highest Federal minimum wage in U.S. history, relative to the average manufacturing wage, was the modern-day equivalent of $12. It took effect in October 1939. However, this only applied to employees engaged in interstate commerce or the production of goods for interstate commerce, so it isn’t clear what percentage of the U.S. workforce was affected by it:
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Note: to convert minimum wage from portion of prevailing average manufacturing wage into approximate present dollar equivalent, multiply the portion by twenty or twenty-one.

However, assuming this correlation:
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(R² = 0.83841884602996, using a power trendline) was sound for the time, this is what the portion of hourly paid wage and salary workers working at or below the highest Federal minimum wage would have looked like before 1978, if the power trendline correlation used for the average hourly wage in the U.S. is applied to the average hourly manufacturing wage (not quite the same thing, especially after 2006):
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I strongly doubt that over 50% of hourly workers in 1969 or over 65% in 1950 had their pay determined by the maximum hourly Federal minimum wage of the time. How many workers actually had their pay determined by the various minimum wages of the time would be interesting to see. Also, it’s not just the Federal minimum wage that matters -state and local minimum wages matter just as much, perhaps, even more.

In the old days, the highest U.S. minimum wage was more restricted in application than it is today, yet, far higher relative to prevailing average wages. The minimum wage only became fully unified for farm and nonfarm workers in 1978, when farm work had become all but irrelevant in America. However, it is clear that the minimum wage has generally had little effect on broad unemployment trends in the United States: the modern era of high over-27 week unemployment began only in 1974: precisely when the minimum wage relative to the prevailing average wage came down from its secular heights in the 1950s and 1960s. Also, note that the largest minimum wage increase in post-WW II U.S. history; that in January 1950, seemed to have no substantial effect on the natural rate of unemployment (it also coincided with, but certainly did not cause, the largest RGDP/worker boom in post-WWII U.S. history).

There were four periods in U.S. history when minimum wage hikes occurred around recessions: the minimum wage hikes around the recession of 1990, which pushed the percentage of hourly paid wage and salary workers paid at or below the minimum wage up to 1986 levels, the minimum wage hikes around the Great Recession, which pushed the percentage of hourly paid wage and salary workers paid at or below the minimum wage up to 1998 levels, and the minimum wage hikes of 1945 and 1974.

Thus, I doubt the Federal minimum wage is very important in explaining broad unemployment trends from 1939 to today. But this is hardly an exhaustive study on this topic, and does not look at the actual prevalence of the various state, Federal, and local minimum wages for the various occupations to which it applied from 1939 to today. Such a study would be very useful in explaining how high a minimum wage would cause an appreciable amount of unemployment, especially for low-skilled workers.

By the way, also see this post for the Federal minimum wage growing faster than productivity for most workers who are actually paid the minimum wage or below, and why the Far Left is generally deceptive in its claims about the minimum wage and productivity. Also, I have noticed a small upward trend with average wages for leisure and hospitality workers in the late 1960s which I’m fairly, but not quite, sure has nothing to do with the expansion of the applicability of the Federal minimum wage:

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Of course, I completely oppose the minimum wage, as well as any other price control during peacetime. The minimum wage, despite its seemingly small effect on U.S. unemployment, is never a good thing on net, as it interferes with the proper functioning of the free market and is fundamentally against Americans’ freedom without any clear net social benefit. The full long-term effects of price controls and their interactions with markets are more difficult to predict than most think.

Update: Here’s a graph of the convergence of the rural and maximum Federal minimum wages. Also, there’s a graph of teen unemployment divided by middle-aged unemployment in the comments. It doesn’t strongly support the idea that the minimum wage ever did much of anything.

Update #2: The minimum wage hike of 1950 (largest of all time) was intended for all workers covered by the fair labor standards act; roughly half of wage and salary workers. So probably something like 30% of wage and salary workers had their pay directly determined by the Federal minimum wage at the time-higher than the level in the 1970s, but nowhere near 70%.