The firm said there were waiting times of up to three and a half hours at the terminal in Folkestone and an hour in Calais.
It tweeted the delays were "due to increased security measures" and said it was working hard to minimise them.
On Thursday, a teenager thought to be from east Africa was killed by freight train near the tunnel in Calais.
The boy is the 11th person to have died in or near the tunnel while trying to reach Britain, since late June.
In a statement, Eurotunnel said: "There is a waiting time of approximately three and a half hours on the terminal.
"We regret that we are currently unable to sell tickets to non-reserved customers.
"We sincerely apologise for the inconvenience this will cause to your journey."
The rail operator also tweeted earlier that services had been affected by a power problem on the national French network but issues were later resolved.
It said security systems would be checked within the Channel Tunnel before any trains were allowed to enter.
There has been a fall in intrusion attempts at Eurotunnel's terminal in Calais after extra security measures were introduced in Europe.
The situation in Calais is part of a wider crisis across Europe, with migrants and refugees heading north from the Mediterranean.
Eurotunnel passengers have faced fresh delays after "migrant activity" led to extra security measures in France.