Ásmundur is a masculine given name. Notable people with the name include:
Ásmundur Ásgeirsson, Icelandic chess player Ásmundur Bjarnason (1927–2024), Icelandic sprinter Ásmundur Einar Daðason, Icelandic politician Ásmundur Friðriksson, Icelandic politician Ásmundur Guðmundsson, Icelandic prelate Asmundur Loptson, Icelandic-Canadian farmer and politician Ásmundur Sveinsson, Icelandic sculptor