The COVID-19 lockdown restrictions affected physical performance and cognitive function in older people as they were confined to their homes. There is an association between physical and cognitive functions. Mild Cognitive Impairment (MCI) is a condition that risks progressing to dementia. This study aimed to identify the relationship between handgrip strength (HGS), Timed Up-and-Go (TUG), and MCI in older people during the COVID-19 pandemic restrictions. The cross-sectional study recruited 464 eligible participants for an interview and anthropometric measurement. The Montreal Cognitive Assessment-Basic (MoCA-B), HGS, and TUG were measured in addition to demographic and health characteristics. A total of 398 participants (85.8%) were found to have MCI when screened with the MoCA-B. Their mean age was 71.09 ± 5.81 years. Forward multiple regression analysis demonstrated that HGS (β = 0.032,p< 0.001), education level (β = 2.801,p< 0.001), TUG (β = −0.022,p= 0.013), Thai Geriatric Depression Score, TGDS (β = −0.248,p= 0.011), and age (β = −1.677,p= 0.019) were associated with MCI. A decrease in HGS and an increased TUG might allow for the early detection of MCI and promote physical training in order to reduce the risk of MCI. Further studies can investigate multidomain indicators for MCI, for example, fine motor skills and pinch strength as components of the motor abilities.