Flight EZY6238 was carrying 170 passengers from Berlin to Bristol on Sunday when it was diverted to Amsterdam's Schiphol airport.
"The aircraft landed routinely and was met by emergency services as per procedure and as precautionary measure only," said an Easyjet spokeswoman.
She described it as a "technical issue" and apologised to those affected.
As well as the pilot, some passengers reported the smell of smoke in the cabin but they were able to disembark the plane normally.
Ellen Braksator wrote on Twitter: "We're all okay, there was a strong smell of smoke on flight deck and emergency landed in Schiphol. No panic."
Nick Canham also tweeted: "I'm a passenger on EZY6238 Berlin-Bristol which just emergency landed in Amsterdam due to strong burning chemical smell."
A replacement Easyjet aircraft was organised to carry passengers onto Bristol after a delay of three hours in Amsterdam.
The airline said it was investigating to determine what caused the smoke.

Netherlands striker Van Persie, 33, had scored the opening goal in the Turkish side's 3-1 win against Akhisar before the first-half injury.
Television pictures showed blood coming through a bandage on his left eye.
"After tests in the hospital this morning I can say my eye itself is undamaged so all good," he said.
He told followers on Instagram that he had torn his eyelid.
Club doctor Burak Kunduracioglu had earlier sought to play down fears the player had suffered a serious eye injury, saying: "He received a blow to the eye and suffered a torn eyelid and bleeding.
"After the investigations we learned that nothing important happened. His condition is good."
The former Arsenal and Manchester United forward joined Fenerbahce from the Old Trafford club in July 2015.

Here are some of your pictures from the 26 beaches ranked as Scotland's "most excellent" for water quality.

The Lynx UK Trust has suggested trial reintroductions in Aberdeenshire, Argyll, Northumberland, Cumbria and Norfolk.
It said the plan has public support and research it commissioned sets out benefits of the big cats' return.
The National Farmers Union (NFU) has previously raised concerns.
Scottish Natural Heritage, which is funded by the Scottish government, has also said reintroductions were "complex" and needed "considerable planning" to meet UK and international guidelines.
Lynx became extinct in the UK 1,300 years ago.
The Lynx UK Trust said 91% of 9,000 respondents to a survey it carried out were in favour of lynx being brought back to help control deer numbers.
AECOM, consultants the trust commissioned to examine the benefits of lynx, have suggested that the cats could benefit eco-tourism as well as prevent deer from damaging crops.
The trust said it now wants to hear views from landowners and farmers.
Dr Paul O'Donoghue, of the trust, said: "Lynx reintroduction is a big step for all of us in the UK and this is the opportunity for a wide range of groups to really understand what it could mean, how they could be affected, and to tell us and the statutory agencies how they feel about it."
Other organisations, including the Scottish Wildlife Trust, Trees for Life and Rewilding Britain, have separately said lynx could form an important part in "rewilding" areas of the UK.
The Cairngorms National Park Authority has in the past weighed up the pros and cons of bringing back the big cats, and also wolves and bears.
Of the three predators, lynx were deemed to have the least negative impact on farmers' businesses.
NFU countryside adviser Claire Robinson said reintroductions raised "big concerns" for farmers in England.
She said: "Any species introduction, particularly if it has not been in this country for hundreds of years, can have a massive impact on the many benefits that the countryside delivers.
"The environment has changed drastically and we do not know how lynx would behave in the current environment.
"But the biggest concern we have would be the impact on farm animals with lynx preying on lambs, poultry and outdoor piglets - those animals are farmers' livelihoods."
An investigation is under way into a pilot's reports of cockpit smoke which led to an Easyjet flight diverting.
[NEXT_CONCEPT]
Fenerbahce's Robin van Persie has reassured supporters that his eye was not damaged after he was carried off the pitch bleeding on Sunday.
[NEXT_CONCEPT]
We actually don't have a picture of Thortonloch beach - yet - so if you have a great shot of this, or if one of our other pictures isn't of quite the right spot, or indeed if you have any other great images from anywhere around Scotland, you can send us your pictures here.
[NEXT_CONCEPT]
Farmers and landowners have been asked for their views on a proposal to bring back lynx to parts of Scotland and England.