The Dane replaced the unimpressive Lukas Podolski in the second half but, having made a big impact during his 23 minutes on the pitch, he had to come off near the end and joins first-choice striker Olivier Giroud on the sidelines.
"Unfortunately he (Bendtner) got injured today and it looks like it is not a question of days, but weeks, with a sprained ankle. I am very sad for us, but for him as well," Arsenal manager Arsene Wenger told reporters.
The victory was wrapped up in added time by Theo Walcott at The Emirates and kept Arsenal one point clear at the top.
However without Bendtner and, more importantly, Giroud for the third round clash at home to in-form Spurs, the Gunners must rely on Podolski who looked rusty and was disappointing in his first league start since September after injury.
"He has not played for four months and he lacked a little bit of the sharpness that's needed up front," Wenger said of the German. "He needed a game and got it today. "It wasn't easy for him because Cardiff were very well organised and worked hard."
Wenger added that he felt sorry for Bendtner, who was almost sold during the close season after being loaned out to Sunderland and Juventus for the two previous campaigns.
"He is a player who has gone through some difficult periods so I just want to give him great credit," said Wenger.
"I told him already today that he is back to the level I want him to be at, and if he continues to develop like that he will come back into the team."
Asked about Bendtner's injury, Wenger said: "Usually he is not a fragile player, he was a bit unlucky. He said he landed on the foot of a Cardiff player and turned his ankle."
Bendtner's ill-starred 2013 saw him fined for drink driving in March, and banned from playing for his country for six months by the Danish FA, and he was also cautioned by police in November for causing damage to his apartment block.
He was on the verge of a transfer to Crystal Palace in the final week of the last transfer window, but was retained when Arsenal's bids for other strikers fell through.
Wenger dismissed the recent booing of Bendtner by sections of the Arsenal crowd as temporary - he was applauded by the fans on Wednesday as he limped around the pitch - and hailed the Dane's return to form, saying he never gave up on him.
In November, Bendtner had said he was "incredibly disappointed" at having to stay with Arsenal and stated his desire to move in the January window but that has now changed.
Asked about the Dane's future at the club, Wenger added: "It is January 1 so we cannot stop him (talking to other clubs) but he says he wants to stay here. If he is focused on staying with us and his job, he is a great striker."