Aneke joined Crewe on an initial one-month loan in September, but saw his playing opportunities limited after being sent off against Stevenage Borough in only his second appearance for Alex.
Crewe boss Steve Davis confirmed the news to the club's official website.
Davis said: "We have agreed with Arsenal to extend his loan. I think Chucks is content here and he wants to play as much as possible.
"He is available again to us and he might even start yet depending on who we have available.
"He is eager to make up for what happened at Stevenage. He wants to make up for the red card and show the Crewe fans what he is capable of."
The 19-year-old England youth international returns to the Crewe squad for Tuesday night's match against Oldham Athletic in his first game back from suspension.