Ahmed, 20, endured a difficult start to his first season in the F1-supporting series, failing to score a point in either Red Bull Ring round or the following pair of races at the Hungaroring.
Ahead of this weekend's fourth round of the series at Silverstone, Carlin announced via social media that "Enaam Ahmed and his sponsors have parted ways with the team" and revealed Barnicoat, who drives for the team in the European Le Mans Series, as his replacement.
Former McLaren F1 junior driver Barnicoat, now a factory driver for the British marque's customer racing programme in GT3s, will be making his first outing in a single-seater since his one and only season in the now-defunct European Formula 3 series in 2016.
That season he finished ninth in the standings with two victories before switching to sportscar racing the following year with campaigns in the Blancpain GT Series (now GT World Challenge Europe) and Pirelli World Challenge (now GT World Challenge America).
Ahmed dabbled in sportscars briefly with an appearance in the Bahrain FIA World Endurance Championship rookie test in December for the G-Drive Racing LMP2 team.
Last year he raced in the All-Japan Formula 3 series, placing third overall, while in 2018 he matched Barnicoat's ninth-place finish in European F3 driving for the same Hitech team.