Astronomical observatories have been identified as substantial contributors to the carbon footprint of astrophysical research. Being part of the collaboration that is currently developing the medium-sized telescopes in the Cherenkov Telescope Array, a ground-based observatory for very-high-energy γ-rays that will comprise 64 telescopes deployed on two sites, we assessed the environmental impacts of one medium-sized telescope on the northern site with a life-cycle assessment. We identified resource use and climate change as having the most significant impacts due to telescope manufacturing and energy consumption during operations. We estimate life-cycle greenhouse gas emissions of 2,660 ± 274 tCO2e for the telescope, 44% of which arise from construction, 1% from on-site assembly and commissioning and 55% from operations over 30 yr. The environmental impacts could be reduced by using renewable energy during construction and operations, using fewer electronic components and metal casting and using recycled materials. We propose complementing the project requirements with environmental budgets as an effective measure for impact management and reductions.