Mr Swan, national political correspondent at the Axios news site, grilled the US president on his handling of the ongoing coronavirus pandemic, among other things, during a car crash interview aired by HBO on Tuesday.
Social media users were quick to pick up on the exchange - which saw Mr Trump rifle through sheets of papers as he defended his management of the Covid-19 crisis and claim he had "done more" to improve the lives of black people in the US than the late civil rights leader John Lewis.
In particular, it was Mr Swan's reactions, which ranged from confusion to sheer disbelief, that captured people's imagination and prompted the creation of an array of hilarious memes.
Here are some of the best ones doing the rounds...
1. Campaign goals
Your campaign goals just say “go viral” pic.twitter.com/qZG3KZMAyg
— emily patterson (@tweetsyall)
2. How's your 2020 going?
— Charlotte Callanan (@evilsocialisttt)
3. The official face of 2020
— Georgia Cattach (@CattachGeorgia)
4. A new meme template
5. Future history
Highschool history students turning to the chapter on 2020 https://t.co/vMVeqcCeKV
— Bethanie Blanchard (@beth_blanchard)
Even Mr Swan's wife, Politico journalist Betsy Woodruff Swan, got in on the action as the trend gathered momentum and memes spanned from Star Wars to Samuel Johnson...
6. For better or worse
Jonathan when I explain why clothes have to go in a pile on the chair instead of in the closet pic.twitter.com/gmSZIjDwG8
— Betsy Woodruff Swan (@woodruffbets)
7. In a confusing galaxy far, far away
8. Confused cat energy
9. The new Samuel Johnson
Jonathan Swan is the new Samuel Johnson pic.twitter.com/HnsKeTvalD
— John Self (@john_self)
10. 2020 cheat sheet
2020 cheat sheet for reacting to things pic.twitter.com/9CPn3x0ZQb
— Sampsa Nuotio (@SampsaNuotio)
In addition to sparking a range of amusing memes, Mr Swan has also won praise for being "one of the best interviewers on the planet" and lauded as an "American hero" for his efforts during the sit-down with Mr Trump.
Mr Trump has been widely denounced for his handling of the coronavirus pandemic, with critics accusing the US president of attempting to downplay its severity and reacting too slowly to the crisis.
The US is currently battling the world's worst coronavirus outbreak and has recorded more than 4.7m infections to date.
More than 155,000 people have meanwhile died nationwide from Covid-19 since the virus was first identified in the country in January.