Amos dislocated a shoulder in the 32-8 defeat by Australia and will have an operation in the next week.
The 22-year-old Dragons wing tweeted: "Operation set for Monday, aiming to be back in February".
"It's unlucky for Hallam... but a great opportunity for Keelan," said Wales assistant coach Neil Jenkins.
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Wales have already selected Cardiff Blues pair Cory Allen and Tomos Williams as injury replacements.
They are waiting to discover the extent of scrum-half Rhys Webb's ankle injury suffered against the Wallabies.
Amos injured his left shoulder stretching for the try-line late in the game against the Wallabies.
But it is not the same shoulder he dislocated playing against England in the 2015 World Cup.
Dragons backs coach Shaun Connor the region were upset by Amos' injury.
"It's devastating for us, but even more so for Hallam," said Connor.
"We're going to miss him, but back-three is a position where we have strength in depth."
Giles has been in outstanding form for Ospreys, scoring eight tries in five appearances for the region this season.
His pace, footwork and small stature - he is 5ft 8in (1.73m) and 12st 1lb (77kg) - have led to comparisons with Wales' record try scorer Shane Williams, which Jenkins acknowledged.
"I think he has a little bit of X-factor about him," said Jenkins.
"He's different to the other guys that we've got. I know a lot of people will point out similarities to Shane.
"He's not the biggest of players but he's quick and he's electric on his feet and he's brave.
"So we'll see how the next couple of weeks go - you never know.
"He's got to take his chance with both hands and show the coaches and the players involved what he's all about.
"He's already done that with the Ospreys and I'm sure he'll do it in our environment."
Wales have called up uncapped 18-year-old Ospreys wing Keelan Giles for the rest of the autumn international series following an injury to Hallam Amos.