Cech has been ruled out for several weeks after sustaining a calf injury in the defeat to Swansea City, meaning that Ospina will be called into rare action over the next few weeks.
The 27-year-old made a high-profile error when selected ahead of Cech for a Champions League group stage match against Olympiacos back in September, scoring an own-goal after dropping a corner in an eventual 3-2 defeat.
Now, the second-choice goalkeeper could not face a more important match in his first fixture back in the team since featuring in an FA Cup tie in January.
Arsene Wenger's side face arch-rivals Tottenham Hotspur at White Hart Lane on Saturday in a North London derby which looks set to be a pivotal point in the title race.
Cech, who has been in imperious form for Arsenal since joining from Chelsea last summer, insists that there are no concerns over Ospina keeping goal in the next few weeks, and backed his teammate to step up to the mark in his absence.
The 33-year-old told the club's website: "David is a very experienced goalkeeper. He has played really well, especially in the FA Cup games where he has been vital.
"I think everybody at the club, including the staff and the players, has big confidence in him because we can see in training and in his international games that he is a great goalkeeper.
“We have full confidence in him and it won’t be a problem. He has enough experience to play this type of game and he has played this game before so I think he will be fine."
Ospina does have experience of being Arsenal's first-choice goalkeeper after playing 21 matches in all competitions in the final five months of last season.
However, the form of his Czech competitor has limited him to just five appearances so far this season, with none of those coming in the Premier League.