Goalscoring opportunities were few and far between in a game which lacked real quality, with both goalkeepers having a largely trouble-free afternoon.
In his programme notes, Wednesday manager Garry Monk highlighted the need for consistency in performance levels after a disappointing run for his team. The midweek defeat at Wigan meant they had lost five out of their previous six league games.
New signing Alessio Da Cruz, who joined loan from Italian club Parma during the week, was named among the Wednesday substitutes.
Millwall's Shaun Williams fired wide during a quiet opening period.
Wednesday's first effort of note came when Jacob Murphy and Kadeem Harris combined to set up Moses Odubajo, whose low drive from the edge of the area flashed narrowly wide of Bartosz Bialkowski's right post.
Mahlon Romeo tried his luck from distance after some uncertain defending from the home side but his effort was well off target.
Adam Reach went close to putting Wednesday ahead a few minutes before the interval when he met a good cross from Harris at the near post, but his glancing header went beyond the far post.
The first substitution of the match came in the 56th minute, when Monk sent on Fernando Forestieri in place of Harris.
Dominic Iorfa threatened inside the area, firing wide of Bialkowski's left post following a corner.
Da Cruz made his debut for the hosts in the 67th minute, coming on as a replacement for Murphy.
Forestieri put a low shot on target but it was straight at Bialkowski, who gathered the ball comfortably.
In time added on, Forestieri tried a speculative effort from distance which was blocked.
Bodvarsson had a chance to nick a win for Millwall at the death when he got on the end of a long ball which had been flicked on, but with just Cameron Dawson to beat, his chip over the keeper cleared the bar.