If the Panama Canal were to close, the major impact would be on the United States. This closure would impact its economy and its military.
If the canal were to close, the US military would become less flexible. Ships that were in the Pacific would not be able to move relatively quickly to the Atlantic and vice versa. This might require the country to maintain a larger navy so as to have more ships in each ocean at all times.
The bigger impact, however, would be economic. The main thing that would happen is that ground transportation would probably become more important. It is likely that the US would continue to import large quantities of goods from Asia. However, those goods would no longer be able to ship directly to the East Coast through the Panama Canal. Instead, they would presumably have to land at West Coast ports and be shipped by rail and/or truck to destinations across the country.
The closing of the Panama Canal would likely not be a huge economic or military blow. It would cause changes and some difficulties, but I do not believe it would be catastrophic.