"It was against Garcia in the first set, when I fell down," Halep told reporters on Tuesday. "I felt pain in the hip. If I'm not 100 percent I don't want to step on the court.
"I'm also exhausted mentally because I gave my everything in that tie but unfortunately we couldn't win. That's why I decided to pull out, because I have to think about my health first.
"It feels bad because I gave everything, I really wanted to win the Fed Cup. I've been very sad the last two days, I just need to recover mentally and physically and then just start again."
Halep's withdrawal means she will now rely on next month's clay court tournaments in Madrid and Rome to prepare for her defence of the French Open title.
Meanwhile, Spain's Garbine Muguruza, the 2016 French Open champion, also pulled out through illness. As a result of the withdrawals, Germany's Angelique Kerber moved into the position of the second seed to get a bye to the second round.
Belarusian Victoria Azarenka will now play Russia's Vera Zvonareva while Croatia's Donna Vekic takes on Italy's Giulia Gatto-Monticone.
(Reporting by Rohith Nair in Bengaluru; Editing by Christian Radnedge)
