Technically, Apple (AAPL) hasn’t sold any iPhone 4s yet — the first sales won’t be recorded until next week. But judging from the pre-orders recorded on Tuesday, it’s heading for its best iPhone launch ever.

According to AT&T (T), Tuesday was “the busiest online sales day in AT&T history.” Despite widely publicized server meltdowns, Apple’s entire first production run had been called for by Tuesday afternoon, and orders placed after 4:30 p.m. EDT were pushed back to June 25 or later. On Apple.com, the iPhone 4 ship-by date has slipped from June 24 to July 2.

In a note to clients issued Wednesday morning, Piper Jaffray’s Gene Munster reminds us that last year and the year before, Apple managed sell 1 million iPhones within three days. Given that roughly 8.4 million iPhone 3Gs owners are eligible for an upgrade under AT&T’s new rules, he  believes an additional 1 million units is “achievable” next weekend, and he is raising his estimate of iPhone sales for Apple’s third fiscal quarter to 9.5 million from 8.5 million (and up from 5.21 million the year before). Based on those estimates, he’s also raising his price target for Apple’s shares to $348 from $330.

But having famously over-estimated iPhone sales a few times before, Munster is probably hedging his bets. We’re inclined to agree with Silicon Alley Insider‘s Dan Frommer, who believes that this launch will be a blow-out. Frommer predicts that by the end of the four-day sales event that begins Thursday, June 24, Apple will announce that it has doubled its previous record and sold 2 million iPhone 4s.

See also:

• Apple Store app crashes on launch
• iPhone 4 (not) available for pre-order
• Japan avoids an iPhone 4 meltdown

[Follow Philip Elmer-DeWitt on Twitter @philiped]