Logan is on the way back from a fractured jaw and his current employers Peterboro see it as an ideal opportunity to get some fitness back.
Posh boss Barry Fry said: 'Richard needs games and this loan move will give him that.'
Town gaffer Quinn told ShrewsWeb: 'Richard's coming into give more options upfront as we're a bit short there at the moment.
'He's a tall quick lad who's scored goals whenever he's played and he'll be a good addition to the squad.'
Logan has previously played for this week's opponents Boston, notching ten times in 30 starts.