Podstanická was born as Regina Šáškyová on 20 March 1928 in the village of Látky in central Slovakia. She was educated at the grammar school in Banská Bystrica and studied physics at the Comenius University, graduating in 1952. Following her graduation she worked at the Slovak Academy of Sciences, focusing on study of perseids at the Skalné Pleso Skalnaté pleso Observatory. On 20 March 1955 Podstanická and her fellow Slovak Academy of Sciences astronomer Alois Paroubek discovered the 1989 Tatry minor planet, becoming the first minor planet discoverers from Slovakia.