Wenger's side booked their place in Thursday's draw when they beat Besiktas 1-0 at the Emirates to squeeze past their Turkish opponents.
Alexis Sanchez's goal just before the break was enough for the North Londonders, but they were handed a tough group when the draw was made.
The Gunners face difficult assignments against Anderlecht, Borussia Dortmund and Galatasaray, and former Gunners great Nicholas thinks Wenger will be forced to act in the transfer market.
The Frenchman has already shelled out around £60 million on the likes of Sanchez, Mathieu Debuchy, David Ospina and Calum Chambers, but they face something of a striker shortage following Olivier Giroud's injury.
The France international broke his foot against Everton last week and will be out until the New Year, and the setback will see Giroud miss the entire group stage.
That fact alone is enough to see Wenger get his wallet out once more, ahead of the September 1 deadline, according to Nicholas.
The Scot told Sky Sports News: "Wenger may just be now thinking that he'll have to go back into the transfer market.
“It's a tough draw, in fact it's very tough. We were in the same pot as Dortmund last seasonn and we lost at the Emirates and at one stage it was a draw. We went to Dortmund and won there, so its difficult to expect [to win] the points at home.
"It’s about picking the points up on the road in the Champions League these days. Galatasaray will be an awkward trip, as it always is, and it depends what time we get them. It’s a tough test for Wenger."
The Gunners two have points this season having followed up their 2-1 win over Crystal Palace last week with a 2-2 draw away to Everton and they play Leicester City this Sunday at the King Power Stadium.