Joe Edwards went closest to finding a winning goal when his second-half drive was tipped onto the bar by Iron keeper Luke Daniels.
Simeon Jackson and Erhun Oztumer also tested Daniels, while visiting stopper Neil Etheridge was rarely troubled, making just a handful of routine saves.
Jon Whitney's men remain 12th in League One, seven points adrift of the play-offs.
Looking to get back on track after Saturday’s defeat at Bolton, the Saddlers made a purposeful start and almost went ahead inside seven minutes.
Isaiah Osbourne swept the ball out to Jason McCarthy who galloped forward down the right and crossed for Simeon Jackson, but his glancing header was kept out one-handed by Luke Daniels.
Scunthorpe responded with Duane Holmes pulling the ball back for Ivan Toney but the Newcastle loanee completely miss-hit his close-range effort.
There were precious few opportunities in the reminder of a cagey first half, with both sides cancelling each other out.
Harry Toffolo created space before firing straight at Neil Etheridge, while Kieron Morris – on for the injured Florent Cuvelier – headed tamely wide from a Joe Edwards cross.
Half-time: Scunthorpe 0-0 Walsall
The Saddlers made a strong start to the second period; Jackson’s shot on the turn from Edwards’ cross was held by Daniels and Morris drilled a rasping 20-yard effort wide.
Only the woodwork denied Walsall on 63 minutes, as Edwards pounced on a Levi Sutton error but Daniels produced a super diving save to turn his right-footed drive onto the bar.
The visitors continued to look the more dangerous, with Oztumer seeing a goalbound strike brilliantly blocked by David Mirfin after a slick move involving Jackson and McCarthy.
Scunthorpe finally began to exert some pressure in the final quarter of an hour.
A Kevin van Veen shot deflected wide and Etheridge made comfortable stops to thwart Madden and Josh Morris from distance.
The Saddlers had been the better side and almost grabbed the goal their dominance deserved with four minutes remaining, when Oztumer’s fierce long-range strike was pushed wide by Daniels.
Full-time: Scunthorpe 0-0 Walsall
Team: Etheridge, O’Connor, Preston, O’Connell, McCarthy, Chambers, Osbourne, Cuvelier (Morris 37’), Edwards, Oztumer (Dobson 89’), Jackson (Bakayoko 76’).
Subs not used: MacGillivray, Randall, Roberts, Moussa.