Puyol made the gesture to his team-mate at the end of their 3-1 win over Manchester United, clearing the way for the Frenchman to take the honour following his return to the side after having a liver tumour removed.
"I can't explain the emotions I have," Abidal told reporters. "It's spectacular. I'm so thankful for the gesture."
Barca were shocked in March when Abidal, who had been in imperious form, was diagnosed with a liver tumour.
After undergoing surgery to have the tumour removed, the 31-year-old returned as a late substitute to a rapturous reception in the Champions League semi-final second leg at the Nou Camp at the start of this month, when Barca secured a 3-1 aggregate win over Real Madrid.
The France international joined the Spanish champions from Olympique Lyon in 2007 and has also played for Ligue 1 sides Lille and AS Monaco.
Barcelona coach Pep Guardiola also praised his captain for a gesture he described as making the club stronger.
"I want to thank Carles publicly for the gesture," he said. "It honours the club and makes us stronger.
"It's another demonstration of the sort of club I understand we are and demonstrates the human qualities of the dressing room."
