The World Group II promotional play-off takes place in Buenos Aires, Argentina from April 20-21.
Robson will be joined by Johanna Konta, Anne Keothavong and Elena Baltacha, the British numbers three, four and six respectively, and led by captain Judy Murray.
"Of course we will miss having Heather with us in Buenos Aires but we are fortunate to have strength in depth and a great mix of youth and experience in our squad," said Murray.
"This is a fantastic opportunity for GB to grab a place in World Group II and we will be doing everything we can to make that happen."
Robson crashed out in the first round of the Katowice Open in Poland on Monday with a loss to Lourdes Dominguez-Lino.
Britain were joint winners of the 16-group Europe/Africa Zone Group I back in February, which put them in the play-off. The winners of that will be promoted to the eight-nation World Group II for 2014.
Britain have not featured in the World Group since 1993.
The men's team shocked Russia at the weekend to reach an unlikely Davis Cup World Group play-off in September.