The 21-year-old former Manchester United youngster has already spent a successful loan spell with BetVictor Northern Premier Division side Radcliffe this season and links up with the Pilgrims for an initial one-month period.
Warren is a right-back by trade, who can also operate at centre-half, and is eligible to make his United debut against the Bucks on Saturday.
Reflecting on Warren's arrival, United boss Craig Elliott told bufc.co.uk: "We have unexpectedly been forced to bring in some competition for the right-side of our defence, as we face a very hectic four weeks of football.
"We were alerted to Tyrell's availability earlier this week and after some very strong recommendations from respected managers and coaches, he ticked all of the boxes.
"He has had a very successful loan period at Radcliffe and add this to an impressive playing background at Manchester United, I am looking forward to working with Tyrell.
"A big thank you goes to Chris Casper at Salford City for all his help and support."