Artell has not featured for the Cobblers since early October having undergone surgery for an Achilles injury.
Town retain a recall option on the former Crewe centre-back after the first 28 days of his loan.
"David has found his opportunities limited," said boss Aidy Boothroyd in a club statement.
"He is fit again now and he needs to be playing regular football. We have a lot of competition for places in defence and it won't do David any good to be sat on the bench.
"He hasn't played for almost five months and he needs games between now and the end of the season.
"This move frees up another position in the squad should we need it moving towards the loan deadline in the next few weeks.
"Wrexham are local to where David lives so it is a logical move for all parties."