Co-administration of coronavirus disease 2019 (COVID-19) and seasonal influenza vaccines has several advantages, has been advocated by various public health authorities and should be seen as an opportunity to increase the uptake of both vaccines. The objective of this survey was to quantify the acceptance of concomitant COVID-19/influenza vaccination and to identify its correlates in a representative sample of Italian adults. Of 2463 participants, a total of 22.9% were favorable to vaccine co-administration, while 16.6% declared their firm unwillingness to receive both vaccines simultaneously. The remaining 60.5% of subjects could be dubbed hesitant to some degree. Compliance with the primary COVID-19 vaccination schedule (adjusted proportional odds ratio (aOR) = 7.78), previous influenza vaccination (aOR = 1.89) and trust in public health institutions (aOR = 1.22) were the main determinants of positive attitudes toward vaccine co-administration. Other significant correlates included age, sex, perceived disease severity and vaccination risk–benefit, being offered a more personalized influenza vaccine and recent seeking for influenza-related information. In Italy, hesitancy toward COVID-19/influenza vaccine co-administration is common and appears to be higher than hesitancy toward either vaccine administered alone. This pattern is multifaceted and requires specific and tailored strategies, with public health institutions playing the central role.