The 34-year-old missed Wednesday's second leg of the Spanish Supercopa against Real Madrid after sustaining the injury in last weekend's 2-1 win at Osasuna.
He told www.fcbarcelona.cat: "Beyond my fractured cheekbone, I also have issues with my lower back. It's overworked.
"I was willing to play at the Bernabeu, but when I got up the morning before the game I wasn't feeling well. Pain was going down my left arm and it was better that I didn't play. I still have that feeling and we'll have to wait."
Brazil wing-back Dani Alves is also doubtful for Sunday due to a left leg problem, but midfielder Thiago has been given the green light to play after missing the Olympics with a tibia injury.
Without the services of Puyol and Alves, Tito Vilanova's side went down 2-1 in the Spanish capital in midweek as Madrid earned a first Supercopa title since 2008. The tie ended 4-4 on aggregate, with Jose Mourinho's team winning on away goals.
Barca have made much the better start in La Liga, though, and head into this weekend's third round of matches with a 100% record and boasting a five-point advantage over the champions.
Mourinho's side started their title defence with a 1-1 home draw against Valencia and then suffered a shock 2-1 loss at Getafe last Saturday.
Gonzalo Higuain, who opened the scoring against Barca in midweek, took a moment to savour the Supercopa success before turning his attention to Sunday's home clash with Granada.
"I think the team set the pace," the Argentina striker said on www.realmadrid.com. "We're happy. We won the first title and that is the important thing. We hurt them when we could. The fans deserved a match like that.
"Now we have Granada's visit and we want to beat them as well. It is true that the most important thing was to win [against Barca] and we did that. Now we must continue along the same path and win on Sunday because the league has just started.
"We cannot slip up, we have to do things as well as we can to get the win."
Like Barca, Real Valladolid and Rayo Vallecano have also made perfect starts to their La Liga campaigns, and will both be in action on Sunday against testing opposition.
Vallecano host Sevilla, while Valladolid travel to San Mames to take on Athletic Bilbao.
Sevilla will be without suspended goalkeeper Diego Lopez, while forward Jose Antonio Reyes has been ruled out for a number of weeks with a shoulder injury.
Athletic will be playing their first match since the loss of Javi Martinez, described by coach Marcelo Bielsa as an "exceptional player" after completing his 40million euros move to Bayern Munich on Wednesday.
Also on Sunday, Espanyol could hand debuts to Simao, Cristian Stuani and Samuele Longo this weekend when they visit Levante.
In Saturday's matches in the Spanish top flight, Celta Vigo play Osasuna, Real Zaragoza tackle Malaga, Deportivo face Getafe and Real Mallorca take on Real Sociedad.
Europa League holders Atletico Madrid will look to continue their unbeaten start to the season at Real Betis on Monday, after competing in the European Super Cup against Champions League winners Chelsea in Monaco on Friday night.
Saturday's La Liga Fixtures
Sunday's La Liga Fixtures
Real Madrid vs Granada
Monday's La Liga Fixtures
Real Betis vs Atletico Madrid