Generally, scholars agree that Shakespeare composed Othello, one of his best known works, in 1604. The earliest documented performance of the play is from later that same year.
Shakespearean plays are usually performed at a rate of about 1,000 lines per hour. The length of Othello is 3,560 lines. At that rate, the play should take approximately three and a half hours to perform.
Performances of the 1600s and 1700s were far from the silent, organized performances of today. Audiences participated in cheering, booing and screaming. One can imagine this might have slowed down the performance some as the performers awaited the audience's silence. The performances could then have run over three and a half hours.
A google search of modern day performances or recordings of performances online show that today's performances take less than the three and a half hours it should take by the rate of 1,000 lines per hour. A quick search showed lengths anywhere from 1 hour 45 minutes to over 2 hours 30 minutes. This could be due to a change to not using all of the original Shakespearean language, speaking some of the lines in more modern language that takes less time, or cutting out entire scenes.
One link at the bottom of my answer lists several media adaptions of this play. Each one contains a length in minutes. These vary between an hour and twenty minutes to two hours and fifteen minutes. The one that probably most directly and accurately translates the action of the play as if it were performed on stage would be the longest, at 2 hours and fifteen minutes.
The second link provides some background as to why the length of the play varied in the time of Shakespeare. It was not his original work.
Most likely, the play would take between 2-3 hours if performed as is on a stage today, therefore it could be performed in one night.