Pye is yet to make his senior debut with Burnley. He joined the Clarets from Manchester United, having originally come through the youth system at Sunderland.
"I need to play men's football and get used to that, so it's the ideal time to come out on loan," Pye told Accrington's website.
"I met the lads before the Oldham game and they all seemed nice, and it will be easy to settle in."
Manager John Doolan said: "I looked at Logan last pre-season, I only needed to see 20 minutes of him. He is a proper left-back, athletic, physical, can defend one-v-one situations, gets forward, and has outstanding qualities, and that's the reason he is at Burnley.
"We didn't want bodies in - but quality players - and we have took our time with them, and we are glad to get Logan over the line."