The pandemic situation in the Czech Republic is now improving. European union plan to introduce so called covid-pass which should allow vaccinated/tested/COVID-19 recovered people to travel freely inside the EU.
Until then (and for citizens of non-EU states), the following rules apply to travelling to the Czech Republic.
From 15 May 2021, vaccinated persons can enter the Czech Republic from Germany, Hungary, Slovenia, Poland, Slovakia and Austria (from 19 May) 22 days after receiving their first shot.
If you are not a citizen of these countries or you are not vaccinated, various restrictions apply depending on the country from which you are travelling.
LOW RISK COUNTRIES (Malta, Iceland, Australia, Israel, South Korea, New Zealand, Singapore, Thailand, Vatican): Travellers can come to the Czech Republic from these countries without any restrictions.
MEDIUM RISK COUNTRIES (Finland, Ireland, Norway, Romania, Portugal (including Madeira and the Azores), the Balearic Islands (Spain), Austria, Bulgaria, Hungary, Italy and Poland): Before traveling to the Czech Republic, foreigners traveling from these countries must (1) fill in an arrival form and (2) undergo an antigen or PCR test, administered no more than 24 hours (antigen) or 72 hours (PCR) before the beginning of the trip and have a written confirmation of the result. (3) It is also mandatory to wear an FFP2 (KN95, N95, P2, DS) respirator everywhere outside the home for 14 days after arrival.
HIGH RISK COUNTRIES (Slovakia, Andorra, France, Belgium, Croatia, Denmark, Estonia, Liechtenstein, Latvia, Luxembourg, the Netherlands, Monaco, Greece, San Marino, Slovenia, Germany, Spain, Switzerland, the Canary Islands (Spain), Cyprus, Lithuania and Sweden + all countries not listed in EXTREME RISK countries): In addition to the MEDIUM RISK countries restrictions, travellers from HIGH RISK countries must (4) undergo a second PCR test (antigen is not sufficient) administered in the Czech Republic, no later than 5 days after arrival. (4) Self-isolation is required until confirmation of a negative test result.
EXTREME RISK COUNTRIES (Botswana, Brazil, Eswatini (Swaziland), India, South Africa, Kenya, Colombia, Lesotho, Malawi, Mozambique, Peru, Tanzania (including Zanzibar and Pemba), Zambia and Zimbabwe): citizens of these countries are prohibited from entering the Czech Republic.
Find more details here.