Centre-back Bartra damaged his hand as a result of broken glass as an explosion shattered windows on the Bundesliga side’s team bus on Tuesday.
Dortmund tweeted “Marc Bartra will be fit again in about four weeks”, with a quote from Thomas Tuchel saying “he would like to play now”.
Bartra could be back for Dortmund’s home game against Hoffenheim – with the two clubs a point apart and fighting over third in the Bundesliga.
He is likely to only miss five games including the second leg against Monaco and German Cup tie with Bayern Munich.
The Spanish defender was taken to the hospital with the Bundesliga side’s Champions League quarter-final with Monaco postponed – before having surgery on Wednesday.
Batrta took to Instagram yesterday to give the thumbs up in a cast and thank fans for their support.
Dortmund eventually lost the postponed match 3-2 – as a Kylian Mbappe and Sven Bender own goal gave the visitors three away goals and a foot in the semi-finals.
Boss Tuchel was not happy the game was played so soon after the attack.
“We weren’t asked at any point. We were told by text message that the decision had been made in Switzerland,” Tuchel said.
“When they told us ‘you’re up tomorrow’, we felt completely ignored.
“They treated it as if a beer can had been thrown at the bus.
“We would have liked more time to take stock,” he added. “This gives you the feeling of impotence, that we have to keep functioning and nothing else matters.
“I encouraged everyone to take the game seriously but football is not the most important thing in the world.”