diff --git a/NAMESPACE b/NAMESPACE
index 81c0fce689..ae54e95d11 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -187,6 +187,8 @@ S3method(seq, ITime)
 S3method(unique, IDate)
 S3method(unique, ITime)
 S3method('[<-', IDate)
+S3method('min', IDate)
+S3method('max', IDate)
 S3method(edit, data.table)
 
 # generics to support custom column formatters
diff --git a/NEWS.md b/NEWS.md
index 8824204aa7..a6fbba8fbf 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -253,6 +253,34 @@
                                    # no inconvenient warning
     ```
 
+    On the same basis, `min` and `max` methods for empty `IDate` input now return `NA_integer_` of class `IDate`, rather than `NA_double_` of class `IDate` together with base R's warning `no non-missing arguments to min; returning Inf`, [#2256](https://github.com/Rdatatable/data.table/issues/2256]. The type change and warning would cause an error in grouping, see example below. Since `NA` was returned before it seems clear that still returning `NA` but of the correct type and with no warning is appropriate, backwards compatible, and a bug fix. Thanks to Frank Narf for reporting, and Matt Dowle for fixing.
+
+    ```R
+    DT
+    #             d      g
+    #        <IDat> <char>
+    # 1: 2020-01-01      a
+    # 2: 2020-01-02      a
+    # 3: 2019-12-31      b
+
+    DT[, min(d[d>"2020-01-01"]), by=g]
+
+    # was:
+
+    # Error in `[.data.table`(DT, , min(d[d > "2020-01-01"]), by = g) :
+    #   Column 1 of result for group 2 is type 'double' but expecting type 'integer'. Column types must be consistent for each group.
+    # In addition: Warning message:
+    # In min.default(integer(0), na.rm = FALSE) :
+    #   no non-missing arguments to min; returning Inf
+
+    # now :
+
+    #         g         V1
+    #    <char>     <IDat>
+    # 1:      a 2020-01-02
+    # 2:      b       <NA>
+    ```
+
 36. `DT[, min(int64Col), by=grp]` (and `max`) would return incorrect results for `bit64::integer64` columns, [#4444](https://github.com/Rdatatable/data.table/issues/4444). Thanks to @go-see for reporting, and Michael Chirico for the PR.
 
 37. `fread(dec=',')` was able to guess `sep=','` and return an incorrect result, [#4483](https://github.com/Rdatatable/data.table/issues/4483). Thanks to Michael Chirico for reporting and fixing. It was already an error to provide both `sep=','` and `dec=','` manually.
diff --git a/R/IDateTime.R b/R/IDateTime.R
index 42a6b289a6..33d04b87c4 100644
--- a/R/IDateTime.R
+++ b/R/IDateTime.R
@@ -71,6 +71,11 @@ unique.IDate =
   x
 }
 
+# define min and max to avoid base R's Inf with warning on empty, #2256
+min.IDate = max.IDate = function(x, ...) {
+  as.IDate(if (!length(x)) NA else NextMethod())
+}
+
 # fix for #1315
 as.list.IDate = function(x, ...) NextMethod()
 
@@ -304,7 +309,7 @@ clip_msec = function(secs, action) {
      stopf("Valid options for ms are 'truncate', 'nearest', and 'ceil'.")
   )
 }
-                           
+
 ###################################################################
 # Date - time extraction functions
 #   Adapted from Hadley Wickham's routines cited below to ensure
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 1d39b2d817..e5a1fb04fc 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -3422,10 +3422,22 @@ test(1083, setkeyv(ans[, list(r = .N), by=key(DT1)], key(ans)), check) # if the
 
 # Tests for #2531. `:=` loses POSIXct or ITime attribute:
 # first test from this SO post: http://stackoverflow.com/questions/15996692/cannot-assign-columns-as-date-by-reference-in-data-table
+set.seed(1)
 dt <- data.table(date = as.IDate(sample(10000:11000, 10), origin = "1970-01-01"))
 dt[, group := rep(1:2, 5)]
 dt[, min.group.date := as.IDate(min(date)), by = group]
-test(1084, class(dt$min.group.date), c("IDate", "Date"))
+test(1084.1, class(dt$min.group.date), c("IDate", "Date"))
+
+# min.IDate on empty input NA, #2256
+# non-optimized grouping first:
+test(1084.2, dt[, min(date[date>"1999-12-01"]), by=group], data.table(group=1:2, V1=as.IDate(c("1999-12-14",NA))))
+test(1084.3, dt[, max(date[date<"1997-08-01"]), by=group], data.table(group=1:2, V1=as.IDate(c(NA,"1997-07-19"))))
+dt[group==2, date:=NA]  # make group 2 an all-NA group
+# GForce grouping with na.rm=FALSE|TRUE on the all-NA group
+test(1084.4, dt[, min(date, na.rm=TRUE), by=group], data.table(group=1:2, V1=as.IDate(c("1997-12-06",NA))))
+test(1084.5, dt[, min(date), by=group],             data.table(group=1:2, V1=as.IDate(c("1997-12-06",NA))))
+test(1084.6, dt[, max(date, na.rm=TRUE), by=group], data.table(group=1:2, V1=as.IDate(c("1999-12-14",NA))))
+test(1084.7, dt[, max(date), by=group],             data.table(group=1:2, V1=as.IDate(c("1999-12-14",NA))))
 
 dt <- data.table(date = as.IDate(sample(10000:11000, 10), origin = "1970-01-01"))
 dt[, group := rep(1:2, 5)]