The club said the Spain international tore a muscle in his left thigh as he dribbled past defender Ignazio Abate in the 38th minute at the Camp Nou stadium.
Iniesta pulled up after the run and leant against the advertising boarding behind the goal line before signaling to the bench he could not play on. He was replaced by Cesc Fabregas.
Barcelona expect Iniesta to be out four weeks, leaving the club without two of its best playmakers with Chile forward Alexis Sanchez also out to injury.
"Andres is a player who has played such a high level for many years now, but sometimes these things happen," coach Pep Guardiola said at the Camp Nou. "He'll recover."
Barcelona surrendered Alexandre Pato's opener after just 24 seconds before going ahead through Pedro Rodriguez and David Villa, but Thiago Silva headed home the equalizer deep into injury-time for the pair to open Group H with one point each.
The Spanish champions are already missing defender Gerard Pique to injury.
Cesc Fabregas replaced Iniesta and alongside Thiago Alcantara will be expected to step in to fill in for the injured player, who has endured such leg injuries in past seasons.
Captain Carles Puyol featured for the first time since May after recovering from knee surgery, although even the centerback's return as a second-half substitute did not stabilize the Catalans struggling defense.
Guardiola began with midfielders Sergio Busquets and Javier Mascherano in the center of his backline and Pato exposed the pair's defensive frailties with most of his touches.
Guardiola said fullback Eric Abidal also struggled with muscle cramping late on as Thiago powered home the equalizer three minutes into injury time. It was Barcelona's latest collapse, coming three days after surrendering a two-goal lead in a 2-2 draw with Real Sociedad.
"Puyol's return is great news, he played well considering it's never easy after so long out to find your rhythm," Guardiola said. "We can admit that defensively we were not adequate. But, I insist that we played a match that was more than acceptable."
Abidal is recovering from liver tumor surgery, while Barcelona did not reinforce its defense in the summer transfer window despite Puyol making only a few appearances after hurting his knee in January
"We try to stay on top of injuries like every seasons but sometimes this happens," Guardiola said. "That's a common muscle injury."