Here is one solution that acts only on character columns.
library(dplyr)
library(stringr)
DF <- data.frame(A = c("A", "B,C", "C"),
B = c("1", "2", "3,4"),
C = rnorm(3))
DF
#> A B C
#> 1 A 1 0.5281151
#> 2 B,C 2 0.8441517
#> 3 C 3,4 -1.7556551
DF <- DF |> mutate(across(where(is.character),
~ifelse(str_detect(.x, ","), NA, .x)))
DF
#> A B C
#> 1 A 1 0.5281151
#> 2 <NA> 2 0.8441517
#> 3 C <NA> -1.7556551
Created on 2022-07-08 by the reprex package (v2.0.1)