A robber apologised to a shop assistant before handcuffing him and making off with the comics.
The theft comes as Spider-Man is in the spotlight after a new movie version of the story had the most successful opening in United States box office history.
It took $114m (£77.6m) in its first three days in the US and Canada, beating the previous record set by the first Harry Potter film.
The comic theft took place on Saturday when the robber asked the shop assistant at Action Comics, Manhattan, to look inside his bag, saying "I have to show you these things".
"I thought he was trying to sell some books, because everyone's always trying to sell books, but then he pulls out a gun," said the assistant, Stuart Bowler.
Mr Bowler said the man was apologetic as he handcuffed him and gathered the rare comics.
"He said, 'I'm sorry. I hate to have to do it this way, but I really need the money,'" Mr Bowler said.
Records
The first edition of The Amazing Spider-Man was published in 1963, and led to a highly successful comic series, cartoon and now feature film.
The live action adaptation of the hero's exploits has topped box office records for the highest takings for a single day and for a weekend.
Spider-Man took $24m (£16m) more than the Harry Potter movie over their respective first three days at cinemas.
It took almost $44m (£29.7m) on Saturday, beating Harry Potter's single day record of $33.5m (£22.8m).
It is now challenging for the title of the year's most successful film - but faces competition from a new Star Wars movie as well as new instalments in the Harry Potter and Lord of the Rings series.
Spider-Man stars Tobey Maguire as student Peter Parker, who gets bitten by a genetically-modified spider and transformed into the webbed superhero.
Kirsten Dunst plays his girlfriend Mary Jane Watson and Willem Dafoe is his arch-enemy the Green Goblin.
The weekend's audience was evenly split between men and women.
The comic's creator Stan Lee is still working at the age of 79, as chairman emeritus of Marvel Comics.
Spider-Man opens in the UK on 14 June.