October 1 – The EU began legal proceedings against the UK after it ignored their deadline to drop controversial sections from its internal market Bill.
October 4 – In the 2020 New Caledonian independence referendum, New Caledonia votes against independence from France.
October 5
Massive protests breakout in Kyrgyzstan following accusations that the October 2020 parliamentary election was "unfair".
COVID-19 pandemic: The number of confirmed cases of COVID-19 passes 35 million worldwide. The news coincides with the World Health Organization estimating that total worldwide cases may be around 760 million - roughly a tenth of the global population.
October 10 – Armenia and Azerbaijan agree on a ceasefire in the ongoing Nagorno-Karabakh conflict.
October 15:
2020 Thai protests: The Government of Thailand declares a "severe" state of emergency banning gatherings of five or more people, initiating a crackdown on demonstrations and imposing media censorship.
President of Kyrgyzstan Sooronbay Jeenbekov resigns from office after weeks of massive protests in the wake of the October 2020 parliamentary election; opposition leader Sadyr Japarov assumes office as both the acting President and Prime Minister of Kyrgyzstan.
October 17 – 2020 New Zealand general election: Jacinda Ardern's Labour Party wins a landslide second term in office, defeating the National Party led by Judith Collins and gaining the country's first parliamentary majority since the introduction of the MMP voting system.
October 19 – COVID-19 pandemic: The number of confirmed cases of COVID-19 passes 40 million worldwide.
October 20 – NASA's OSIRIS-REx spacecraft briefly touches down on Bennu, becoming the agency's first probe to retrieve samples from an asteroid, with its cargo due for return to Earth in 2023.
October 22 – The Geneva Consensus Declaration on Promoting Women's Health and Strengthening the Family is signed by government representatives from 34 countries.
October 23
At the end of an 11-year demining process, the Falkland Islands are declared free of land mines, 38 years after the end of the 1982 war.
Israel and Sudan agree to normalise relations, marking the fifth Israel–Arab peace deal.
October 26 – NASA confirms the existence of molecular water on the sunlit side of the Moon, near Clavius crater, at concentrations of up to 412 parts per million.
October 29 – The International Organization for Migration (IOM) confirms the death of least 140 migrants who drowned off the coast of Senegal on a vessel bound for the Spanish Canary Islands. It is the deadliest shipwreck of 2020 so far.
October 30
2020 Aegean Sea earthquake: A magnitude 7.0 earthquake hits Turkey and Greece, killing at least 81 people and injuring nearly 1,000.
COVID-19 pandemic: The number of confirmed cases of COVID-19 passes 45 million worldwide.
October 31 – Typhoon Goni makes landfall in the Philippines, becoming the strongest landfalling tropical cyclone in history, displacing hundreds of thousands of people and killing dozens of people in the region.
India
31 October - Uttar Pradesh Chief Minister Yogi Adityanath announced that a law to curb 'Love Jihad' would be passed by his government.
