How much profit has Apple’s leading App Store raked in? According to estimates from Piper Jaffray analyst Gene Munster—about $189 million since inception.

That’s what Munster says Apple gained in gross profit, which is about 1% of the company's $33.7 billion in overall gross profit in the same timeframe.

Munster derived the figure based on CEO Steve Jobs’ announcement at the recent Worldwide Developers Conference that Apple has paid $1 billion to app developers and that there have been 5 billion free and paid app downloads since the store first went live in September of 2008. Based on the 70% cut provided to app developers, that implies a $1.4 billion gross revenue taken in.

From the note: Using a pricing scheme similar to iTunes, with 70% ($1.04) to the developer, $0.20 plus 2% of the ASP ($0.23) to the credit card company, and 1% ($0.02) per app for processing (storage & delivery), we estimate Apple's App Store gross margin on revenue from paid apps ($428m since launch) is about 44%, or $189m in gross profit. This does not factor in the roughly $81m Apple has spent since launch to store and deliver the 4b free apps that have been downloaded.

Munster additionally estimates that 81% of apps are free, with the remaining 19% paid at an average price of $1.49. The average price of the top 30 iPad apps, meanwhile, is $4.66, which he says will drive overall app store prices up over time.

As for volume, Munster estimates iPhone, iPad and iPod Touch users collectively download more than 16.6 million apps per day. That’s almost twice the 8.9 million tracks per day downloaded from iTunes.