Prevent content from expanding grid items

By default, a grid item cannot be smaller than the size of its content.

Grid items have an initial size of min-width: auto and min-height: auto.

You can override this behavior by setting grid items to min-width: 0, min-height: 0 or overflow with any value other than visible.

From the spec:

6.6. Automatic Minimum Size of Grid Items

To provide a more reasonable default minimum size for grid items, this specification defines that the auto value of min-width / min-height also applies an automatic minimum size in the specified axis to grid items whose overflow is visible. (The effect is analogous to the automatic minimum size imposed on flex items.)

Here's a more detailed explanation covering flex items, but it applies to grid items, as well:

• Why don't flex items shrink past content size?

This post also covers potential problems with nested containers and known rendering differences among major browsers.

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To fix your layout, make these adjustments to your code:

.month-grid {
  display: grid;
  grid-template: repeat(6, 1fr) / repeat(7, 1fr);
  background: #fff;
  grid-gap: 2px;
  min-height: 0;  /* NEW */
  min-width: 0;   /* NEW; needed for Firefox */
}

.day-item {
  padding: 10px;
  background: #DFE7E7;
  overflow: hidden;  /* NEW */
  min-width: 0;      /* NEW; needed for Firefox */
}

jsFiddle demo

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1fr vs minmax(0, 1fr)

The solution above operates at the grid item level. For a container level solution, see this post:

• Who does minmax(0, 1fr) work for long elements while 1fr doesn't?

The previous answer is pretty good, but I also wanted to mention that there is a fixed layout equivalent for grids, you just need to write minmax(0, 1fr) instead of 1fr as your track size.