The COVID-19 pandemic has tremendously affected higher education systems in Russia and all over the world, forcing to transform curriculum into an online format, which is a challenge for all the educational process participants. The current study discusses the implementation of online learning amid the COVID-19 pandemic in the Russian higher education context and investigates the challenges experienced by university teachers during this period to define their readiness for online education. To address the above-mentioned issues, a study was conducted in Peter the Great St. Petersburg Polytechnic University. A variety of methods of scientific and pedagogical research were used including systematic structural analysis, synthesis, work with research papers, the generalization of experience and experimental work, observation, surveys, etc., with 87 university teachers asked to respond to several sets of questions describing their online teaching experience after the launch of online education amid the COVID-19 pandemic. The analysis of the participants' answers helped to identify the following main challenges experienced by university teachers: computer literacy level, the university electronic environment and support, academic staff readiness and students' readiness for online learning, the last two being the most important hindering the implementation of the efficient online education process. It was also underlined by most respondents that methodological work of a teacher in a digital educational environment differs from conventional teaching methods. Thus, psychological, technological, methodological support and teachers' professional development programs are of vital importance to minimize the negative impact of the rapid changes of the educational process and to ensure efficient online education.