(Feb 2017) As of Google I/O 2016, developers no longer need to export to Excel nor create a new Sheet w/the desired formatting, so the other answers are now dated. You can now format cells using the Google Sheets API. Here's a short Python example that bolds the 1st row (assuming the file ID is SHEET_ID and SHEETS is the API service endpoint):

DATA = {'requests': [
    {'repeatCell': {
        'range': {'endRowIndex': 1},
        'cell':  {'userEnteredFormat': {'textFormat': {'bold': True}}},
        'fields': 'userEnteredFormat.textFormat.bold',
    }}
]}

SHEETS.spreadsheets().batchUpdate(
        spreadsheetId=SHEET_ID, body=DATA).execute()

I also made a developer video on this subject if that helps (see below). BTW, you can do the same in Ruby (see its API quickstart sample) or any other language supported by the Google APIs Client Libraries.

The Sheets API provides features not available in older releases, namely giving developers programmatic access to a Sheet as if you were using the user interface (frozen rows, cell formatting[!], resizing rows/columns, adding pivot tables, creating charts, etc.). If you're new to the API, I've created a few videos with somewhat more "real-world" examples:

• Migrating SQL data to a Sheet plus code deep dive post
• Formatting (text in) cells using the Sheets API plus code deep dive post
• Generating slides from spreadsheet data plus code deep dive post

To see what else you can do with Google Sheets via its REST API or Google Apps Script, check out my other videos. As you can tell, the Sheets API is primarily for document-oriented functionality as described above, but to perform file-level access such as import/export, copy, move, rename, etc., use the Google Drive API instead.

In that case, I thought that the property of pattern might be required to be set. So in this case, how about modifying your request of repeatCell as follows?

Modified request:

{
  "repeatCell": {
    "range": {,,,}, // Please set range.
    "cell": {
      "userEnteredFormat": {
        "numberFormat": {
          "type": "CURRENCY",
          "pattern": "[$¥-411]#,##0.00"  // <--- Added
        }
      }
    },
    "fields": "userEnteredFormat.numberFormat"  // or "fields": "userEnteredFormat"
  }
}

Note:

• In my environment, when above modified request is used for the batchUpdate method, I could confirm that "Currency" was checked.

References:

• RepeatCellRequest- NumberFormat

It isn't clear from your question just what kind of data you want to get. Do you want to retrieve the values as they're formatted in the Google Sheets UI? If so, then use the spreadsheets.values.get API. The parameter valueRenderOption controls how the values are formatted. By default, the value is FORMATTED_VALUE, which will return the data as it's formatted in the Sheets UI. Other values are listed on the ValueRenderOption reference page. See the Basic Reading sample for more information.

If you want to retrieve the information about the format itself, use the spreadsheets.get API. Format information is in the response's CellData (at sheets.data.rowData.values), in both the userEnteredFormat and effectiveFormat fields.

I perform a test regarding this, use this sample code to see if that helps.

I'm currently using this scopes:

SCOPES = ['https://www.googleapis.com/auth/drive.file', 
            'https://www.googleapis.com/auth/drive',
            'https://www.googleapis.com/auth/spreadsheets' ]

And the sample code I'm using is:

    try:
        service = build('sheets', 'v4', credentials=creds)

        # Call the Sheets API and the sheet ID for "Sheet1"
        # the ID is not the name of the sheet but a number.
        call_sheet_with_format = service.spreadsheets().get(spreadsheetId=SPREADSHEET_ID).execute()
        sheets_with_format = call_sheet_with_format.get('sheets', '')
        sheet_id = sheets_with_format[0].get("properties", {}).get("sheetId", 0)

        request_body = {
            'requests': [
                {
                    'updateCells': {
                        'range': {
                            'sheetId': sheet_id
                        },
                        'fields':'userEnteredFormat'
                    }
                }
            ]
        }

        request = service.spreadsheets().batchUpdate(spreadsheetId=SPREADSHEET_ID, body=request_body)
        response = request.execute()



    except HttpError as err:
        print(err)

Or you can get the sheetId directly in the Google Sheet:

And remove this part of the

        sheets_with_format = call_sheet_with_format.get('sheets', '')
        sheet_id = sheets_with_format[0].get("properties", {}).get("sheetId", 0)