Eighteen-year-old Smith will go straight in to the squad to face Wealdstone today.
Assistant-manager Gary MacDonald saw him play on Tuesday, describing him as a "big strong no-nonsense centre-half, who is good on the ball".
Smith signed a two-year scholarship with Barnet in 2015.
After loan spells at Staines Town and Three Bridges, he signed a professional contract with the Bees in April 2017.
Smith made his senior debut for Barnet in August 2017 against AFC Wimbledon in the EFL Trophy.