The 26-year-old was the only player to receive serious injuries in the blast, which happened on April 11 as the team travelled to the Signal Iduna Park for the first leg of their Champions League quarter-final against AS Monaco.
Bartra updated fans on his recovery on both his Twitter and Instagram pages, posting a picture of his arm in a black and yellow cast - the colours of Dortmund's strip - while giving a thumbs up.
He said in a tweet: "Happy with the progress! Happy with the evolution and soon starts the hard work to be back as soon as possible!"
The Spain international is expected to be out for at least a month due to the injury.