Magnesium alloys are promising candidates for biodegradable medical implants which reduce the necessity of second surgery to remove the implants. Yttrium in solid solution is an attractive alloying element because it improves mechanical properties and exhibits suitable corrosion properties. Silver was shown to have an antibacterial effect and can also enhance the mechanical properties of magnesium alloys. Measurements of microhardness and electrical resistivity were used to study the response of Mg–4Y and Mg–4Y–1Ag alloys to isochronal or isothermal heat treatments. Hardening response and electrical resistivity annealing curves in these alloys were compared in order to investigate the effect of silver addition. Procedures for solid solution annealing and artificial aging of the Mg–4Y–1Ag alloy were developed. The corrosion rate of the as-cast and heat-treated Mg–4Y–1Ag alloy was measured by the mass loss method. It was found out that solid solution heat treatment, as well artificial aging to peak hardness, lead to substantial improvement in the corrosion properties of the Mg–4Y–1Ag alloy.