Sources in the Mhow police station said that the victim was sleeping near an overbridge when she was abducted.
Earlier this year, Indore was adjudged India's cleanest city for the third straight year in the central government's cleanliness survey.
The deceased identified as pre-final year student Bhurelal Waskel was living in a rented accommodation in Ajaybag area of the city.
Man of the Match Mayank Agarwal said it was a dream come true for him to play for India and produce this kind of performance.
Paceman Mohammed Shami claimed four wickets as Bangladesh were bowled out for 213 in the final session of play.
Mushfiqur went into the break undefeated on 53 off 114 balls in the company of Mehidy Hasan Miraj, batting on 38 off 54 balls.
India declared their first innings at overnight score of 493 for 6 to let their pace attack make effective use of the conducive conditions.
Before the start of day three's play of the first Test against Bangladesh, India decided to declare their innings overnight with a lead of 343 runs here at the Holkar Cricket Stadium.
Seeing the opener celebrating his 150, the captain gestured Mayank to keep swinging and score a double hundred next and the latter was quick to respond.
Speaking at the end of the day's play, Agarwal said that not thinking too much about failure and things which aren't in his control has helped him rise to the challenges he has faced in his career.
At close of play, Jadeja and Umesh Yadav (25 batting), who once again hit three sixes to show his big-hitting prowess, were at the crease.
The 28-year old Karnataka batsman is the second highest run-getter in Tests this year and is behind Australia's Steve Smith who has 774 runs from seven innings.
Earlier, the three Indian pacers consistently bowled at 140 kmph, with seam, swing and bounce making life miserable for Bangladeshi batsmen.
India's slip fielding was below-par on the day with Ashwin paying the price for Rahane's twin bloopers in the slip cordon that gave Rahim and Mahmudullah Riyad (10) reprieve.
He picked the wicket of captain Mominul Haque to register his 250th wicket.