diff --git a/.changelog/26081.txt b/.changelog/26081.txt
new file mode 100644
index 000000000..16259f821
--- /dev/null
+++ b/.changelog/26081.txt
@@ -0,0 +1,3 @@
+```release-note:bug
+docker: Fixed a bug where very low resources.cpu values could generate invalid cpu weights on hosts with very large client.cpu_total_compute values
+```
diff --git a/drivers/docker/driver.go b/drivers/docker/driver.go
index 102d0947d..6fb6a6413 100644
--- a/drivers/docker/driver.go
+++ b/drivers/docker/driver.go
@@ -951,17 +951,25 @@ func memoryLimits(driverHardLimitMB int64, taskMemory drivers.MemoryResources) (
 // maxCPUShares is the maximum value for cpu_shares in cgroups v1
 // https://github.com/torvalds/linux/blob/v6.15/kernel/sched/sched.h#L503
 const maxCPUShares = 262_144
+const minCPUShares = 2
 
 // cpuResources normalizes the requested CPU shares when the total compute
 // available on the node is larger than the largest share value allowed by the
 // kernel. On cgroups v2, Docker will re-normalize this to be within the
 // acceptable range for cpu.weight [1-10000].
 func (d *Driver) cpuResources(requested int64) int64 {
+	if requested < minCPUShares {
+		return minCPUShares
+	}
 	if d.compute.TotalCompute < maxCPUShares {
 		return requested
 	}
 
-	return int64(float64(requested) / float64(d.compute.TotalCompute) * maxCPUShares)
+	result := int64(float64(requested) / float64(d.compute.TotalCompute) * maxCPUShares)
+	if result < minCPUShares {
+		return minCPUShares
+	}
+	return result
 }
 
 func (d *Driver) createContainerConfig(task *drivers.TaskConfig, driverConfig *TaskConfig,
diff --git a/drivers/docker/driver_linux_test.go b/drivers/docker/driver_linux_test.go
index fe79fece5..3f6d3bd19 100644
--- a/drivers/docker/driver_linux_test.go
+++ b/drivers/docker/driver_linux_test.go
@@ -129,6 +129,12 @@ func TestDockerDriver_NormalizeCPUShares(t *testing.T) {
 	driver.compute.TotalCompute = maxCPUShares + 1
 	must.Eq(t, 262143, driver.cpuResources(maxCPUShares))
 
+	driver.compute.TotalCompute = maxCPUShares + 1
+	must.Eq(t, 2, driver.cpuResources(2))
+
+	driver.compute.TotalCompute = maxCPUShares + 1
+	must.Eq(t, 2, driver.cpuResources(1))
+
 	driver.compute.TotalCompute = maxCPUShares * 2
 	must.Eq(t, 500, driver.cpuResources(1000))
 	must.Eq(t, maxCPUShares/2, driver.cpuResources(maxCPUShares))
diff --git a/drivers/shared/executor/executor_linux_test.go b/drivers/shared/executor/executor_linux_test.go
index 438311f67..9dc94487f 100644
--- a/drivers/shared/executor/executor_linux_test.go
+++ b/drivers/shared/executor/executor_linux_test.go
@@ -1089,6 +1089,9 @@ func TestExecutor_clampCPUShares(t *testing.T) {
 	le.compute.TotalCompute = MaxCPUShares + 1
 	must.Eq(t, 262143, le.clampCpuShares(MaxCPUShares))
 
+	le.compute.TotalCompute = MaxCPUShares + 1
+	must.Eq(t, 2, le.clampCpuShares(1))
+
 	le.compute = cpustats.Compute{TotalCompute: MaxCPUShares * 2}
 	must.Eq(t, 500, le.clampCpuShares(1000))
 	must.Eq(t, MaxCPUShares/2, le.clampCpuShares(MaxCPUShares))