The pair clashed heads in the Blues' 3-1 Capital One Cup quarter final win at Derby on Tuesday, forcing Zouma to be carried off.
The defender should be available for Chelsea's trip to Stoke on Monday, though, after being assessed at the iPro Stadium.
Cech had come for a corner at the end of the first half and clattered into Zouma as he punched clear.
The goalkeeper has worn headgear since fracturing his skull in a collision with Reading's Stephen Hunt in 2006 and believes it prevented further injury at Derby.
He said: "I was a bit concerned because we collided with a heavy clash
I think it was lucky he hit my helmet because the impact would have been much bigger
I think the helmet saved him, me as well
Because he hit most of the helmet and took away a little bit of the impact.
"He's fine, the medical staff did really well to assess the situation
In this kind of clash you never know
He did not look so good to continue
Obviously it was the right choice
Now he is all clear hopefully."
Chelsea were frustrated at the slow arrival of the stretcher bearers after Zouma was poleaxed.
Cesc Fabregas and Eden Hazard ran to help carry the stretcher and Cech revealed club doctor Eva Carneiro had asked for them three times before they arrived.
He said: "Eva was saying at least three times prior to that through the radio, 'Bring the stretcher'
We could hear it
I think that was why everyone was upset with the call
We heard 'Bring the stretchers', 'Bring the stretchers' and 'Bring the stretchers' but nobody was coming.
"I think that's why the players got involved
Overall I think the situation was handled well, everybody did the right thing
The main objective was to make sure the player was safe and he is safe."
Hazard, Filipe Luis and Andre Schurrle completed a comfortable win for the Blues to move them into the last four.
Craig Bryson pulled a goal back for Derby to make it 2-1 before Jake Buxton was sent off with 12 minutes left.
Boss Steve McClaren admitted he may appeal the dismissal, otherwise the defender will be suspended for Saturday's visit of Norwich.
The Rams are third in the Sky Bet Championship and Bryson insisted the festive period is vital to their promotion hopes.
"It's this period which will show you where you are come the end of the season," he told Rams Player.
"If we're strong and pick up results we'll be up there but everyone knows how hard the Championship is and how much every team wants the points
We need to be on top of our game."
Chelsea were in control for long spells and Bryson felt Buxton's red card knocked the stuffing out of Derby.
He added: "We were disappointed to lose the game
The sending off killed us a wee bit, we got back to 2-1 and the team and everyone in the stadium got a lift but the sending off killed it.
"We need to dust ourselves down, take confidence we matched the best team in England and take it into Saturday against Norwich."
Source : PA
Source: PA