Assombalonga spurned a great chance with a header at the death for Forest while keeper Karl Darlow had to be on hand to deny Lions striker Mathias Ranegie from close range.
The goalless draw means Forest remain unbeaten, and top of the Championship, while Millwall move on to 11 points for the campaign after defeats to Ipswich then Reading.
It took Forest just 55 seconds to have their first sight of goal in what would be a tight match at the Den but, after Michail Antonio had cut in from the left, he fired wide from 18 yards.
Assombalonga tussled with Carlos Edwards on five minutes and, as he wriggled clear, the Lions full-back fell awkwardly and had to be stretchered off.
Ranegie tried to thread Jermaine Easter through on goal after 13 minutes but the forward was stopped in his tracks by a cynical-looking trip from Michael Mancienne – all in blue appealed for a penalty but referee Graham Scott shook his head.
Henri Lansbury picked out Jack Hunt on the right but Lions defender Mark Beevers did well to divert his well-hit cross out for a corner.
On 25 minutes Lansbury found Assombalonga from a free-kick but the Championship’s leading scorer could only head straight at David Forde from six yards.
A last-ditch tackle from Beevers then prevented Lansbury from racing through on goal as Forest began to crank up the pressure.
Antonio, Forest’s most dangerous player, whipped in a cross from the left on 31 minutes, which Forde had to claw away from underneath his crossbar.
Martyn Woolford met Shaun Williams’ cross to head straight at Forest stopper Darlow nine minutes before the break, in a rare goal attempt from the hosts.
Kelvin Wilson got his head in the way of Williams’ rasping strike seven minutes after the break as Millwall started the second period on the front foot.
Darlow could only flick Ed Upson’s cross into the path of Woolford on 56 minutes and from a narrow angle the Lions midfielder drilled inches wide.
But the visiting goalkeeper made a super stop with 64 minutes gone when he instinctively stuck out a leg to keep out Ranegie’s close-range volley.
Substitute Ricardo Fuller latched on to his own flick on 15 minutes from time before firing tamely at Darlow before Upson dragged well wide two minutes later.
At the other end, Antonio headed Chris Burke’s cross over the top on 83 minutes and Assombalonga could not get the power required on his close-range header four minutes later, so the contest ended level.