The Hoops ace warns that Kane Hemmings could end a stellar home record tonight.
On paper, it should be a routine win for Ronny Deila's side, who are 27 points clear of tonight's opponents in sixth, but Mackay-Steven isn't so sure.
Dundee marksman Hemmings has netted 15 goals from 24 SPL starts - 20 in all competitions - and the Celtic man says that victory cannot be a foregone conclusion against a player like that.
“Dundee have been slowly improving in the last few years and they now have a distinct style,” Mackay-Steven told the club's official website.
“They have some good players in the wide areas and up front Kane Hemmings has scored quite a lot of goals for them, and he is a threat with his pace on the break. It won’t be an easy game at all as Paul Hartley has got them playing really well."
Deila and co will be aiming to put a mixed February behind them by kicking off March with three points.
They finished the month with a 1-1 draw away to Hamilton, after starting it with a defeat to closest rivals Aberdeen, but victories against Inverness and Ross County in between was okay.
Tonight could prove their sixth straight home win, having not dropped any points at Celtic Park since late 2015, but in-form Hemmings will be out to end that.