Amphiphilic copolymers containing polydimethylsiloxane (PDMS) and polyethylene glycol methyl ether (MPEG) were obtained via an azide-alkyne cycloaddition reaction between alkyne-functionalized copolymer of MPEG methacrylate and azide-functionalized PDMS. “Click” reactions were carried out with an efficiency of 33–47% increasing grafting degrees. The grafted copolymers were able to carry out the micellization and encapsulation of active substances, such as vitamin C (VitC), ferulic acid (FA) and arginine (ARG) with drug loading content (DLC) in the range of 2–68% (VitC), and 51–89% (FA or ARG). In vitro release studies (phosphate buffer saline, PBS; pH = 7.4 or 5.5) demonstrated that the maximum release of active substances was mainly after 1–2 h. The permeability of released active substances through membrane mimicking skin evaluated by transdermal tests in Franz diffusion cells indicated slight diffusion into the solution (2–16%) and their remaining in the membrane. Studies on the selected carrier with FA showed no negative effect on cell viability, proliferation capacity or senescence, as well as cell apoptosis/necrosis differences or cell cycle interruption in comparison with control cells. These results indicated that the presented micellar systems are good candidates for carriers of cosmetic substances according to physicochemical characterization and biological studies.