"Life goes on," Kaja Tael told a news conference in Brussels on Monday just days before Estonia is due to take over the rotating presidency of the EU Council from Malta.
She was speaking a week after the formal Brexit talks started in Brussels.
Tael, Estonia's Permanent Representative to the EU, described Brexit as the "elephant in the room", but added that the presidency will be "happy" to leave the talks "in the competent hands" of the European Commission and the EU's chief Brexit negotiator, Michel Barnier.
She said, "One thing we do want to see is for member states to be kept full informed as the negotiations progress.
"But life goes on and, for the Estonian presidency, Brexit is not one of our priorities. Yes, it is a hugely important issue and, I am afraid that it is going to occupy our everyday lives for the next two years.
"But I want to stress that this is not something that is going to trouble our presidency of the EU."
It will be the first time Estonia has held the presidency, which helps steer the EU agenda for a period of six months.
The ambassador outlined those issues which she says will top the Estonian agenda, including security and countering the current terror threat in Europe.
On this, she said, "This is currently the issue of most concern to all Europeans and there are some things we can do at EU level, for example, establishing the databases necessary to help tackle the threat from terrorism."
Another priority, she told reporters, will be tackling the ongoing migration issue although, here, she cautioned, "There are no quick fixes and we cannot offer any promises."
"The migration crisis, international terrorism and organised crime are all sources of instability and risk."
Climate change and, in particular, ensuring that the recommendations of the Paris agreement are enforced, will also be high on the Estonian work programme for the six months of its term.
Tael said, "I very much regret the decision taken by the United States to withdraw from the Paris agreement but it has become clear that the EU is still 100 per cent committed to the accord and also to reducing greenhouse gas emissions by 2030 by 40 per cent.
"The focus now will be sorting out the devil in the details and this is an issue we'll give our full attention to."
The diplomat, who will play a key role in implementing the Estonian agenda before it hands over the reins on 1 January 2018, said that pushing through the EU's digital agenda legislation will be another important aspect of its work from 1 July.
Tael, formerly Estonia's ambassador to Germany and also the UK, said, "The digital agenda is certainly an area where our presidency can provide added value."
She said, "The future of the world is digital. A prosperous and sustainable Europe embraces technological transformation by boldly seizing the opportunities offered through digitilisation."
Tael added, "Estonians are hugely pragmatic people who like to take the bull by the horns and that's something we'll do with the presidency.