The development striker follows in the footsteps of keeper Luke Coddington, who has made three appearances for the Welsh club.
Coddington’s stay runs until December 10, while Pyke, 19, will be at the Racecourse Ground through to Boxing Day.
He could make his debut in tonight’s game at Wrexham’s fellow former Football League club Lincoln City.
Dean Keates’ side are 15th in the table.
Pyke, from Chapeltown in Leeds, joined Town from Rothwell Juniors as an Under 12.
A regular at Under 23 level, scoring five times this season, he has yet to play a first-team game, but featured for David Wagner’s side in pre-season.
He watched Wrexham’s 3-1 home win over National League leaders Forest Green Rovers on Saturday, when Coddington saved a penalty.
Both Town’s football operations chief Stuart Webber and academy boss Steve Weaver have worked at Wrexham in the past.
Town’s Under 23 coach Frankie Bunn, whose side went down 4-2 at Birmingham City in their latest Professional Development League clash, said: “Rekeil has been in and around the development side for the last couple of years.
“The next stage in his development is to play against senior players on a regular basis in front of a crowd at major stadia.
“It will certainly be a step up for him in terms of the competition and environment, where managers want to win games.
“Football is often about solving new problems on the pitch.
“Rekeil is a well-built boy with pace and perhaps he’s bullied defenders at Under 18 and Under 23 level a few times.
“Now he’ll have to learn other ways to get on the ball and get in behind against opponents that may be stronger than him.
“We feel this is the next step for him and will be a good experience at Wrexham.”
Town have two other development players out on loan.
Keeper Tadhg Ryan is at Radcliffe Borough and defender Fraser Horsfall at their Northern Premier League First Division North rivals Trafford.
Both deals end this week.